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Araştırma Makalesi

Araştırma Makalesi

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1981

David

**A**.**Floering**
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2019

We introduce the notion of

**a**Khovanov–**Floer**theory. We prove that every page (after E1) of the spectral sequence accompanying**a**Khovanov–**Floer**theory is**a**link invariant, and that an oriented link cobordism induces**a**map on each page which is an invariant of the cobordism up to smooth isotopy rel boundary.
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Konferans Makalesi

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2010

**A**.

**Floercken**

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2004

We define

**a****Floer**-homology invariant for knots in an oriented three-manifold, closely related to the Heegaard**Floer**homologies for three-manifolds defined We set up basic properties of these invariants, including an Euler characteristic calculation, and**a**description of the behavior under connected sums.
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2016

It has been

**a**central open problem in Heegaard**Floer**theory whether cobordisms of links induce homomorphisms on the associated link**Floer**homology groups We show that sutured**Floer**homology, together with the above cobordism maps, forms**a**type of TQFT in the sense of Atiyah. Hence, link**Floer**homology is**a**categorification of the multi-variable Alexander polynomial.
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2015

The Rabinowitz–

**Floer**homology for**a**class of semilinear problems and applications In this paper, we construct**a**Rabinowitz–**Floer**type homology for**a**class of non-linear problems having a starshaped potential; we consider some equivariant
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2014

This defines

**a**function Θ on H1(Y;Z), which was introduced by Turaev as an analogue of Thurston norm. We will give**a**lower bound for this function using the correction terms in Heegaard**Floer**homology. As**a**corollary, we show that**Floer**simple knots in L-spaces are genus minimizers in their homology classes, hence answer questions of Turaev and Rasmussen
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2013

We prove an isomorphism of these invariants with Ozsváth–Szabó’s Heegaard–

**Floer**invariants for certain extremal spinc structures. As applications, we give new calculations of Heegaard–**Floer**homology of certain classes of 3-manifolds, and**a**characterization of Juhász’s sutured**Floer**
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2019

We build

**a**bridge between**Floer**theory on open symplectic manifolds and the enumerative geometry of holomorphic disks inside their Fano compactifications
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2005

Let L⊂S3 be

**a**link. We study the Heegaard**Floer**homology of the branched double-cover Σ(L) of S3, branched along L. For the general case, we derive**a**spectral sequence whose E2 term is**a**suitable variant of Khovanov's homology for the link L, converging to the Heegaard**Floer**homology of Σ(L).
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2012

We consider

**a**stabilized version of HF̂ of**a**3-manifold Y (i.e. the U=0 variant of Heegaard**Floer**homology for closed 3-manifolds). We give**a**combinatorial algorithm for constructing this invariant, starting from a Heegaard decomposition for Y, and give a topological proof of its invariance
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2017

We define and investigate spectral invariants for

**Floer**homology HF(H,U:M) of an open subset U⊂M in T⁎M, defined by Kasturirangan and Oh as**a**direct limit of**Floer**homologies of approximations. We define**a**module structure product on HF(H,U:M) and prove the triangle inequality for invariants with respect to this product.
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2016

In this paper, we use

**a**perturbed version of the Rabinowitz–**Floer**homology to find solutions to PDE’s with jumping nonlinearities.
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2019

We identify the Grothendieck group of the tangle

**Floer**dg algebra with**a**tensor product of certain Uq(gl1|1) representations. Under this identification, up to**a**scalar factor, the map on the Grothendieck group induced by the tangle**Floer**dg bimodule associated to**a**tangle agrees
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2011

**A**link surgery spectral sequence in monopole

**Floer**homology To

**a**link L⊂S3, we associate

**a**spectral sequence whose E2 page is the reduced Khovanov homology of L and which converges to

**a**version of the monopole

**Floer**We define

**a**mod 2 grading on the spectral sequence which interpolates between the δ-grading on Khovanov homology and the mod 2 grading on

**Floer**homology We also derive

**a**new formula for link signature that is well adapted to Khovanov homology.

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2017

3-sphere graph manifolds and relate them to the property of not being

**a**Heegaard–**Floer**L-space. , using foliations, and using Heegaard–**Floer**homology. The fact that Heegaard–**Floer**methods can be used to detect families of slopes on the boundary of**a**Seifert fibred manifold combines with certain conjectures
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2008

On the Heegaard

**Floer**homology of**a**surface times a circle We make**a**detailed study of the Heegaard**Floer**homology of the product of**a**closed surface Σg of genus g with S1. We show that in this case HF∞ is closely related to the cohomology of the total space of**a**certain circle bundle over the Jacobian torus of Σg, and furthermore This is the first example known to the authors of torsion in Z-coefficient Heegaard**Floer**homology.
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2018

We establish

**a**relationship between Heegaard**Floer**homology and the fractional Dehn twist coefficient of surface automorphisms. Specifically, we show that the rank of the Heegaard**Floer**homology of**a**3-manifold bounds the absolute value of the fractional Dehn twist coefficient of**a**surface automorphism to guarantee that the associated contact manifold is tight or overtwisted, respectively.
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2019

Fixing

**a**weakly unobstructed Lagrangian torus in**a**symplectic manifold X, we define**a**holomorphic function W known as the**Floer**potential. We construct**a**canonical**A**∞-functor from the Fukaya category of X to the category of matrix factorizations of W. It provides**a**unified way to construct matrix factorizations from Lagrangian**Floer**theory.
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2012

The

**Floer**homology of**a**cotangent bundle is isomorphic to loop space homology of the underlying manifold, as proved by Abbondandolo and Schwarz, Salamon In this paper we show that in the presence of**a**Dirac magnetic monopole which admits**a**primitive with at most linear growth on the universal cover, the**Floer**homology in atoroidal free homotopy classes is again isomorphic to loop space homology.
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2020

In particular, it is unobstructed, formal, and its

**Floer**and de Rham cohomologies coincide. Our result implies that the smooth fibers of**a**large class of singular Lagrangian fibrations are unobstructed and their**Floer**and de Rham cohomologies This is**a**step in the SYZ and family**Floer**cohomology approaches to mirror symmetry.
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2020

We prove

**a**general form of the wall-crossing formula which relates the disk potentials of monotone Lagrangian submanifolds with their**Floer**-theoretic behaviour away from**a**Donaldson divisor.
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2015

Area-preserving diffeomorphisms of

**a**2-disc can be regarded as time-1 maps of (non-autonomous) Hamiltonian flows on R/Z×D2. We examine the dynamics relative to such braid classes and define**a**new invariant for such classes, the braid**Floer**homology. This refinement of**Floer**homology, originally used for the Arnol'd Conjecture, yields**a**Morse-type forcing theory for periodic points of area-preserving
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2018

In the description of the instanton

**Floer**homology of**a**surface times a circle due to Muñoz, we compute the nilpotency degree of the endomorphism u2−64
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2012

Lagrangian

**Floer**homology in**a**general case has been constructed by Fukaya, Oh, Ohta and Ono, where they construct an**A**∞-algebra or an**A**∞-bimodule from They developed obstruction and deformation theories of the Lagrangian**Floer**homology theory.
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2019

This proof also gives

**a**strategy to prove Baldwin and Levine's conjecture that δ–graded knot**Floer**homology is mutation–invariant. Let L′ be**a**link obtained from L by mutating the tangle T. Finally, we give sufficient conditions for**a**general Khovanov-**Floer**theory to be mutation–invariant.
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Dergi Makalesi

Dergi Makalesi

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2012

Aerated kaolin floc formation was studied in

**a**continuous-flow, laboratory-scale system, and the flocs were separated from aqueous solution by flotation Microbubbles were generated by the depressurisation of dissolved air in water, and flocculation was achieved in**a**Floc Generator Reactor (FGR). Flocculation–flotation studies were performed using**a**non-ionic polymer (920SH SNF-**Floerger**®) added to**a**suspension flow (4 L/min) at an air/solid rate
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2006

In earlier articles, the authors introduced invariants for closed, oriented three-manifolds, defined using

**a**variant of Lagrangian**Floer**homology in the
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Araştırma Makalesi

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1996

We use path integral methods and topological quantum field theory techniques to investigate

**a**generic classical Hamiltonian system. In particular, we show that**Floer's**instanton equation is related to**a**functional Euler character in the quantum cohomology defined by the topological
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2010

We define the reduced Khovanov homology of an open book (S,ϕ), and identify

**a**distinguished “contact element” in this group which may be used to establish Our construction generalizes the relationship between the reduced Khovanov homology of**a**link and the Heegaard**Floer**homology of its branched double cover Lastly, we investigate**a**comultiplication structure on the reduced Khovanov homology of an open book which parallels the comultiplication on Heegaard**Floer**
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2007

For each positive integer n, Khovanov and Rozansky constructed an invariant of links in the form of

**a**doubly-graded cohomology theory whose Euler characteristic We use Lagrangian**Floer**cohomology on some suitable affine varieties to build**a**similar series of link invariants, and we conjecture them to be equal to
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2017

We modify the construction of knot

**Floer**homology to produce**a**one-parameter family of homologies tHFK for knots in S3.
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2008

An Ozsváth–Szabó

**Floer**homology invariant of knots in**a**contact manifold Using the knot**Floer**homology filtration, we define invariants associated to**a**knot in**a**three-manifold possessing non-vanishing**Floer**co(homology) classes In the case of the Ozsváth–Szabó contact invariant we obtain an invariant of knots in**a**contact three-manifold.
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2019

According to the Arnold conjectures and

**Floer's**proofs, there are non-trivial lower bounds for the number of periodic solutions of Hamiltonian differential equations on**a**closed symplectic manifold whose symplectic form vanishes on spheres. We use an iterated graph construction and Lagrangian**Floer**homology to show that these lower bounds also hold for certain Hamiltonian delay equations.
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2012

**A**combinatorial spanning tree model for knot

**Floer**homology We iterate Manolescu’s unoriented skein exact triangle in knot

**Floer**homology with coefficients in the field of rational functions over Z/2Z. The result is

**a**spectral sequence which converges to

**a**stabilized version of δ-graded knot

**Floer**homology.

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2005

We study the intersections of gradient trajectories and holomorphic discs with Lagrangian boundary conditions in cotangent bundles, and give

**a**construction of Piunikhin–Salamon–Schwarz isomorphisms in Lagrangian intersections**Floer**homology.
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2014

In their recent preprint, Baldwin, Ozsváth and Szabó defined

**a**twisted version (with coefficients in**a**Novikov ring) of**a**spectral sequence, previously defined by Ozsváth and Szabó, from Khovanov homology to Heegaard–**Floer**homology of the branched double cover along**a**link.
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2018

We define and study

**a**bigraded knot invariant whose Euler characteristic is the Alexander polynomial, closely connected to knot**Floer**homology. The invariant is the homology of**a**chain complex whose generators correspond to Kauffman states for a knot diagram.
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2010

We construct an invariant of certain open four-manifolds using the Heegaard

**Floer**theory of Ozsváth and Szabó. We show that there is**a**manifold X homeomorphic to R4 for which the invariant is non-trivial, showing that X is an exotic R4.
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2016

Generalizing

**a**concept of Lipshitz, Ozsváth and Thurston from Bordered**Floer**homology, we define D-structures on algebras of unital operads, which can also be interpreted as**a**generalization of a seemingly unrelated concept of Getzler and Jones.
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2017

In the 2016 preprint “Kauffman states, bordered algebras, and

**a**bigraded knot invariant,” Ozsváth and Szabó introduced**a**set of algebraic constructions in the spirit of bordered Heegaard**Floer**homology. “Quivers,**Floer**cohomology, and braid group actions” (2002).
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1996

The structure of perrottetianal B,

**a**sacculatane-type diterpene dialdehyde, which has previously been isolated from the liverwort Porella perrottetiana The distribution of the known sesqui- and diterpenoids, as well as bis-bibenzyl derivatives, in Swiss liverworts Barbilophozia lycopodioides, B.**floerkei**Perrottetin E,**a**cyclic bis-bibenzyl isolated from Jungermannia comata showed inhibitory activity for thrombin (IC50 18 μM).
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2008

We use Heegaard

**Floer**homology to obtain bounds on unknotting numbers. This is**a**generalisation of Ozsváth and Szabó's obstruction to unknotting number one.
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2021

We show that Ozsváth–Szabó's bordered algebra used to efficiently compute knot

**Floer**homology is**a**graded flat deformation of the regular block of a q-presentable
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2017

We introduce an invariant of tangles in Khovanov homology by considering

**a**natural inverse system of Khovanov homology groups. This work suggests**a**strengthened relationship between Khovanov homology and Heegaard**Floer**homology by way of two-fold branched covers that we formulate in**a**series of conjectures.
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2020

On closed symplectically aspherical manifolds, by using

**Floer**homology, Schwarz proved**a**classical result, i.e., that the action function of a nontrivial
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2013

We prove that

**Floer**cohomology of cyclic Lagrangian correspondences is invariant under transverse and embedded composition under**a**general set of assumptions
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2006

Using the Heegaard

**Floer**homology of Ozsváth and Szabó we investigate obstructions to**a**rational homology sphere bounding a four-manifold with a definite
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2020

**A**Gelfand-Cetlin system is

**a**completely integrable system defined on

**a**partial flag manifold whose image is

**a**rational convex polytope called

**a**Gelfand-Cetlin Motivated by the study of Nishinou-Nohara-Ueda [24] on the

**Floer**theory of Gelfand-Cetlin systems, we provide

**a**detailed description of topology of Gelfand-Cetlin

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1990

**A**field theoretical discussion of the complex constructed by

**Floer**in order to prove the Arnold conjecture concerning

**a**Morse theory for the fixed point