A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study computes SL(2,C) Floer cohomology for surgeries on knots.
Develops Floer cohomology for 4-manifolds with involutions and links.
Study new conjectures linking knot volume and knot cohomology.
We define an invariant of based transverse links, as a well-defined element inside the equivariant Heegaard Floer cohomology of its branched double cover, defined by Lipschitz, Hendricks, and Sarkar. We prove the naturality and functoriality of equivariant Heegaard Floer cohomology for branched double covers of a…
Study knot Floer cohomology using hyperbolic metrics and wrapped Fukaya categories.
Develops equivariant Seiberg-Witten-Floer cohomology for 3-spheres.
We construct smooth concordance invariants of knots which take the form of piecewise linear maps from [0,1] to R, one for each n greater than or equal to 2. These invariants arise from sl(n) knot cohomology. We verify some properties which are analogous to those of the invariant Upsilon (which arises from knot Floer ho…
New invariant from knot diagrams helps classify knots.
Paper establishes an isomorphism between Fukaya category and bordered knot Floer homology.
New knot concordance invariants from Seiberg-Witten theory bound slice genus.
We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using singular instantons. We then show that the latter homology i…
We prove that twisted correction terms in Heegaard Floer homology provide lower bounds on the Thurston norm of certain cohomology classes determined by the strong concordance class of a 2-component link in . We then specialise this procedure to knots in , and obtain a lower bound on their geomet…
Seidel and Smith introduced the graded fixed-point symplectic Khovanov cohomology group Kh_{symp,inv}(K) for a knot K inside S^{3}, as well as a spectral sequence converging to the Heegaard Floer homology-hat group for the connected sum of the double branched cover with a copy of S^{2}xS^{1}. The E^{1}-page of this spe…
Defines log Floer cohomology for symplectic surfaces with a degenerate part.
We generalize Lagrangian Floer cohomology to sequences of Lagrangian correspondences. For sequences related by the geometric composition of Lagrangian correspondences we establish an isomorphism of the Floer cohomologies. We give applications to calculations of Floer cohomology, displaceability of Lagrangian correspond…
We consider Lagrangian Floer cohomology for a pair of Lagrangian submanifolds in a symplectic manifold M. Suppose that M carries a symplectic involution, which preserves both submanifolds. Under various topological hypotheses, we prove a localization theorem for Floer cohomology, which implies a Smith-type inequality f…
Knot Floer homology matches fixed point Floer for fibred knots.
Various Seiberg-Witten Floer cohomologies are defined for a closed, oriented 3-manifold; and if it is the mapping torus of an area-preserving surface automorphism, it has an associated periodic Floer homology as defined by Michael Hutchings. We construct an isomorphism between a certain version of Seiberg-Witten Floer …
New algebraic method for knot Floer homology computation.
We define an integer graded symplectic Floer cohomology and a Fintushel-Stern type spectral sequence which are new invariants for monotone Lagrangian sub-manifolds and exact isotopes. The Z-graded symplectic Floer cohomology is an integral lifting of the usual Z_Sigma(L)-graded Floer-Oh cohomology. We prove the Kunneth…
Study links with annuli using sutured Floer homology.
These are notes from lectures given at the Clay Institute Summer School on "Floer homology, gauge theory and low-dimensional topology" (Budapest, 2004). The first part describes as background some of the geometry of symplectic fibre bundles and their monodromy. The second part, overviewing joint work with Paul Seidel, …
New spectral sequences define knot invariants.
Proves properties of instanton knot Floer homology and connected sum formula.
New colored knot Floer homology defined using infinite full twists.
We define an integer graded symplectic Floer cohomology and a spectral sequence which are new invariants for monotone Lagrangian sub-manifolds and exact isotopies. Such an integer graded Floer cohomology is an integral lifting of the usual Floer-Oh cohomology with $Z_{\Si (L)}$ grading. As one of applications of the sp…
Algorithm calculates knot Floer homology for a specific knot type.
The paper classifies knot Floer complexes of low width, simplifying knot bases.
Formula for Heegaard Floer multicurves of double tangles from knot complements.
Study shows rank of knot Floer homology detects Hopf links and classifies second smallest links.
Study of knot Floer homology and its relation to Heegaard Floer homology via equivariant surgery.
New link detection results using knot and link Floer homology.
Knot Floer homology stabilizes with twists.
The objective of this paper is to clarify the relationships between the quantum D-module and equivariant Floer theory. Equivariant Floer theory was introduced by Givental in his paper ``Homological Geometry''. He conjectured that the quantum D-module of a symplectic manifold is isomorphic to the equivariant Floer cohom…
Lecture notes on Heegaard Floer homology for 3-manifolds and knots.
Study shows how knot Floer homology and bordered Floer theory are linked.
Positive braid knots have simple knot Floer homology.
New homomorphisms from knot Floer homology help classify knots.
This note explores two questions: (1) Which bigraded groups arise as the knot Floer homology of a knot in the three-sphere? (2) Given a knot, how many distinct knots share its Floer homology? Regarding the first, we show there exist bigraded groups satisfying all previously known constraints of knot Floer homology whic…
We exhibit an infinite family of knots with isomorphic knot Heegaard Floer homology. Each knot in this infinite family admits a nontrivial genus two mutant which shares the same total dimension in both knot Floer homology and Khovanov homology. Each knot is distinguished from its genus two mutant by both knot Floer hom…
In this paper, we introduce a sequence of invariants of a knot K in S^3: the knot Floer homology groups of the preimage of K in the m-fold cyclic branched cover over K. We exhibit the knot Floer homology in the m-fold branched cover as the categorification of a multiple of the Turaev torsion in the case where the m-fol…
New method connects knot Floer homology with bordered Floer homology.
Study on knots proves inequality in Floer homology.
Injective map proven in knot Floer homology for strong homotopy-ribbon concordances.
Given a closed, connected, oriented 3-manifold with positive first Betti number, one can define an instanton Floer group as well as a quilted Lagrangian Floer group. The quilted Atiyah-Floer conjecture states that these cohomology groups are isomorphic. We initiate a program for proving this conjecture.
Floer theory constructs filtrations on quantum cohomology for symplectic manifolds.
Algorithm computes knot Floer complex for knots of thickness one.
Develops Floer theory for 3-manifold covers using equivariant structures.