• Floer homology can tell whether a knot is fibered, and this has led to proofs that both knot Floer homology and Khovanov homology can positively identify a small handful of knots: the unknot, the trefoils, the figure eight, and the cinquefoil. (mpg.de)
  • A further seminar devoted to applications of Ozsvath and Szabo's theory to low dimensional topology and, in particular, to its relationship with Khovanov homology is planned for SS05. (ethz.ch)
  • And the situation is at least as bad for Khovanov homology. (columbia.edu)
  • Khovanov homology associates to a link \(L\) in the three-sphere a bigraded vector space arising as the homology groups of an abstract chain complex defined combinatorially from a link diagram. (temple.edu)
  • When \(L\) is realized as the closure of a braid (or more generally, of a "balanced" tangle), one can use a variant of Khovanov's construction due to Asaeda-Przytycki-Sikora and L. Roberts to define its sutured Khovanov homology, an invariant of the tangle closure in the solid torus. (temple.edu)
  • Sutured Khovanov homology distinguishes braids from other tangles (joint with Ni) and detects the trivial braid conjugacy class (joint with Baldwin). (temple.edu)
  • In this talk, I will describe some of the representation theory of the sutured Khovanov homology of a tangle closure. (temple.edu)
  • These character varieties discussed above are related to singular instanton knot Floer homology, Khovanov homology and Casson-Lin invariants. (unr.edu)
  • Shortly after, Levine and Zemke proved the analogous result for ribbon concordances between links and their Khovanov homology. (ucdavis.edu)
  • We determine the structure of the Khovanov homology groups in homological grading 1 of positive links. (hu-berlin.de)
  • More concretely, we show that the first Khovanov homology is supported in a single quantum grading determined by the Seifert genus of the link, where the group is free abelian and of rank determined by the Seifert graph of any of its positive link diagrams. (hu-berlin.de)
  • In particular, for a positive link, the first Khovanov homology is vanishing if and only if the link is fibered. (hu-berlin.de)
  • We also show that several infinite families of Heegaard Floer L-space knots have vanishing first Khovanov homology. (hu-berlin.de)
  • Let n∈ Z + . We provide two short proofs of the following classical fact, one using Khovanov homology and one using Heegaard-Floer homology: if the closure of an n-strand braid σ is the n-component unlink, then σ is the trivial braid. (syr.edu)
  • In this talk, we will show that the map induced by a ribbon concordance on knot Floer homology is an injection. (rutgers.edu)
  • The key input is a classification of genus-1 knots which are "nearly fibered" from the perspective of knot Floer homology. (mpg.de)
  • The aim of the present article is to exhibit stronger restrictions on such knots, arising from knot Floer homology. (princeton.edu)
  • Ozsváth, P & Szabó, Z 2005, ' On knot Floer homology and lens space surgeries ', Topology , vol. 44, no. 6, pp. 1281-1300. (princeton.edu)
  • I am interested in pseudoholomorphic curves, Lagrangian submanifolds, mirror symmetry and knot contact homology. (google.com)
  • We prove a formula for the Alexander polynomial of a knot K in terms of the augmentation polynomial of K (which is defined via the knot contact homology of K). The proof involves studying pseudoholomorphic curves in the cotangent bundle of Euclidean 3-space, with boundary components mapping to the zero section and to a Lagrangian that is diffeomorphic to the knot complement. (google.com)
  • These invariants reside in monopole knot homology and closely resemble Heegaard Floer invariants due to Lisca-Ozsváth-Stipsicz-Szabó, but their construction directly involves the contact topology of the knot complement and so many of their properties are easier to prove in this context. (mit.edu)
  • The pillowcase and traceless representations of knot groups, II: A Lagrangian-Floer theory in the pillowcase (with M. Hedden and P. Kirk), J. Symplect. (unr.edu)
  • In a recent result, Zemke showed that a ribbon concordance between two knots induces an injective map between their corresponding knot Floer homology. (ucdavis.edu)
  • Embedded Contact Homology of Prequantization Bundles. (cnrs.fr)
  • In this talk, I'll discuss recent work with John Baldwin in which we show for the first time that both invariants can also detect non-fibered knots, including 5_2, and that HOMFLY homology detects infinitely many knots. (mpg.de)
  • Peter Ozsvath and Zoltan Szabo recently constructed a Floer homology theory leading to invariants of 3-manifolds and knots. (ethz.ch)
  • We review the construction of Heegaard-Floer homology for closed three-manifolds and also for knots and links in the three-sphere. (ems.press)
  • In an earlier paper, we used the absolute grading on Heegaard Floer homology HF + to give restrictions on knots in S 3 which admit lens space surgeries. (princeton.edu)
  • Heegaard Floer Homology is a useful invariant for three manifolds, and it has many variants that can be used to study four dimensional cobordism and knots in three spheres. (umich.edu)
  • denote the group of knots in homology spheres that bound homology balls, modulo smooth concordance in homology cobordisms. (projecteuclid.org)
  • In this thesis we apply techniques from the bordered and sutured variants of Floer homology to study Legendrian knots. (mit.edu)
  • Second, we use monopole Floer homology for sutured manifolds to construct new invariants of Legendrian knots. (mit.edu)
  • More advanced minicourses will cover such topics as Heegaard-Floer homology, knots and BPS states, characteristic classes for manifold bundles, BPS states and spectral networks, Higgs bundles, and applications of Floer homology. (ias.edu)
  • In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology. (wikipedia.org)
  • Andreas Floer introduced the first version of Floer homology, now called Lagrangian Floer homology, in his proof of the Arnold conjecture in symplectic geometry. (wikipedia.org)
  • We intend to give a comprehensive introduction to its main building blocks: Lagrangian Floer homology and Gromov's theory of pseudo-holomorphic disks. (ethz.ch)
  • Then, I will make an analogy to the Lagrangian Floer Homology to define the ingredients of the Heegaard Floer Homology. (umich.edu)
  • For instanton Floer homology, the gradient flow equations is exactly the Yang-Mills equation on the three-manifold crossed with the real line. (wikipedia.org)
  • I will expose some work in collaboration with John Baldwin, Irving Dai, and Steven Sivek showing that the lattice cohomology of an almost-rational singularity is isomorphic to the framed Instanton Floer homology of its link. (mcmaster.ca)
  • There are more complicated operations on the Floer homology of a cotangent bundle that correspond to the string topology operations on the homology of the loop space of the underlying manifold. (wikipedia.org)
  • In this talk, we describe some applications of link Floer homology to the topology of surfaces in 4-space. (gatech.edu)
  • We explain how to compute the symplectic homology of a complement of a smooth Donaldson-type divisor in a closed symplectic manifold, in terms of (absolute and relative) Gromov-Witten invariants of the manifold and the divisor. (google.com)
  • Inspired by Heegaard Floer theory Nemethi introduced a combinatorial invariant of complex surface singularities (lattice cohomology) that was recently proved to be is isomorphic to Heegaard Floer homology. (mcmaster.ca)
  • The analogue of Froyshov''s correction term in this setting is an integer-valued invariant of homology cobordism whose mod 2 reduction is the Rokhlin invariant. (cam.ac.uk)
  • In work in progress with Santana Afton and Tye Lidman, we show that the d-invariant of Y, a homology cobordism invariant of homology spheres defined using Heegaard Floer homology, is bounded above by a linear function of the word length of a corresponding gluing element in the Torelli group for any fixed, finite generating set when the genus is larger than 2. (dartmouth.edu)
  • We define Pin(2)-equivariant Seiberg-Witten Floer homology for rational homology 3-spheres equipped with a spin structure. (cam.ac.uk)
  • Moreover, we show the d-invariant is bounded for homology spheres corresponding to various large families of mapping classes. (dartmouth.edu)
  • Using tools from Heegaard Floer homology, we show that the cokernel of this map, which can be understood as the non-locally-flat piecewise-linear concordance group, is infinitely generated and contains elements of infinite order. (projecteuclid.org)
  • Floer also developed a closely related theory for Lagrangian submanifolds of a symplectic manifold. (wikipedia.org)
  • Symplectic Floer Homology (SFH) is a homology theory associated to a symplectic manifold and a nondegenerate symplectomorphism of it. (wikipedia.org)
  • We describe a connection between Nielsen fixed point theory and symplectic Floer homology for surfaces. (edu.pl)
  • Fukaya--Oh--Ohta--Ono in Remark 31.18 of their recent paper http://arxiv.org/abs/1209.4410 say there is such an approach, but it is based on the machinery of their books "Lagrangian intersection Floer theory: anomaly and obstruction I - II" which are beyond my current knowledge. (mathoverflow.net)
  • For Hamiltonians that are quadratic at infinity, the Floer homology is the singular homology of the free loop space of M (proofs of various versions of this statement are due to Viterbo, Salamon-Weber, Abbondandolo-Schwarz, and Cohen). (wikipedia.org)
  • Joshua Greene receives the 2023 Levi L. Conant Prize for the article "Heegaard Floer homology", Notices of the AMS , 68 (2021), No. 1, pp. 19-33. (ams.org)
  • It aims to relate seemingly distinct Floer homological, algebraic, and geometric properties of a closed 3-manifold Y. In particular, it predicts a 3-manifold Y isn't "simple" from the perspective of Heegaard-Floer homology if and only if Y admits a taut foliation. (uga.edu)
  • A third construction, also due to Floer, associates homology groups to closed three-dimensional manifolds using the Yang-Mills functional. (wikipedia.org)
  • As an application, we show that the 3-dimensional homology cobordism group has no elements of order 2 that have Rokhlin invariant one. (cam.ac.uk)
  • Finally, I will define the hat version of Heegaard Floer chain complex and homology. (umich.edu)
  • As shown by Morita, every integral homology 3-sphere Y has a Heegaard decomposition into two handlebodies where the gluing map along the boundary is an element of the Torelli subgroup of the mapping class group of the boundary composed with the standard gluing map for the 3-sphere. (dartmouth.edu)
  • Adam Levine : Heegaard Floer Homology and. (duke.edu)
  • The symplectic version of Floer homology figures in a crucial way in the formulation of the homological mirror symmetry conjecture. (wikipedia.org)
  • For the cotangent bundle of a manifold M, the Floer homology depends on the choice of Hamiltonian due to its noncompactness. (wikipedia.org)
  • We will talk about how link Floer homology can be used to give lower bounds, as well as some techniques for computing non-trivial examples. (gatech.edu)
  • The symplectic Floer homology of a Hamiltonian symplectomorphism of a compact manifold is isomorphic to the singular homology of the underlying manifold. (wikipedia.org)
  • Floer homology is a novel invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology. (wikipedia.org)
  • Loosely speaking, Floer homology is the Morse homology of the function on the infinite-dimensional manifold. (wikipedia.org)
  • We use the Hamiltonian $H(x,t)=\epsilon\cdot f(x)$ for some Morse--Smale function $f:M\to\mathbb R$. Then the generators of the Floer chain complex correspond to the critical points of $f$, so it remains to identify the differential with the Morse--Smale differential. (mathoverflow.net)
  • Floer exploits an $\mathbb S^1$-symmetric in the problem to show that any part of the Floer differential which does not come from a Morse--Smale flow line must carry a free $\mathbb S^1$-action. (mathoverflow.net)
  • SFH is the homology of the chain complex generated by the fixed points of such a symplectomorphism, where the differential counts certain pseudoholomorphic curves in the product of the real line and the mapping torus of the symplectomorphism. (wikipedia.org)
  • A pseudo-Anosov flow on a closed 3-manifold dynamically represents a face F of the Thurston norm ball if the cone on F is dual to the cone spanned by homology classes of closed orbits of the flow. (columbia.edu)
  • A Floer chain complex is formed from the abelian group spanned by the critical points of the function (or possibly certain collections of critical points). (wikipedia.org)
  • Floer homology is the homology of this chain complex. (wikipedia.org)
  • The proof is via defining the "Floer homology" $HF(M;H)$ of $M$ with respect to any $1$-periodic Hamiltonian $H:M\times\mathbb S^1\to\mathbb R$, which is then shown to be independent of $H$ (and thus can be written as $HF(M)$). There are some technicalities involved in this definition (Novikov rings, transversality, bubbling, etc.), which for the purposes of this question I would like to ignore. (mathoverflow.net)
  • In this article we give a uniform proof why the shift map on Floer homology trajectory spaces is scale smooth. (intlpress.com)
  • The Gromov compactness theorem is then used to show that the differential is well-defined and squares to zero, so that the Floer homology is defined. (wikipedia.org)
  • If the symplectomorphism is Hamiltonian, the homology arises from studying the symplectic action functional on the (universal cover of the) free loop space of a symplectic manifold. (wikipedia.org)
  • Moreover, we completely classify the contact structures with contact surgery number one on S¹xS², the Poincaré homology sphere, and the Brieskorn sphere Σ(2,3,7). (hu-berlin.de)