Related papers: Locally equivalent Floer complexes and unoriented …

We construct absolute and relative versions of Hamiltonian Floer homology algebras for strongly semi-positive compact symplectic manifolds with convex boundary, where the ring structures are given by the appropriate versions of the…

We study the Ozsv\'{a}th-Szab\'{o}-Thurston transverse invariant in combinatorial link Floer homology for certain transverse cables $\mathscr{L}_{p,q}$ of transverse link $L$ in $S^3$. Transverse cables $\mathscr{L}_{p,q}$ are constructed…

A natural family of potentially 2-torsion elements in the integer homology cobordism group consists of splices of knots with their mirrors. We show that such 3-manifolds have locally trivial involutive Floer homology. We show some related…

We make use of the action of $H_1(Y)$ in Heegaard Floer homology to generalize the Ozsv\'ath-Szab\'o correction terms for $3$-manifolds with standard $\operatorname{HF}^\infty$. We establish the basic properties of these invariants:…

A slice-torus invariant is an $\mathbb{R}$-valued homomorphism on the knot concordance group whose value gives a lower bound for the 4-genus such that the equality holds for any positive torus knot. Such invariants have been discovered in…

We define and study a family of link invariants $\mathit{HFK}_{n}(L)$. Although these homology theories are defined using holomorphic disc counts, they share many properties with $sl_{n}$ homology. Using these theories, we give a framework…

Localization of Floer homology is first introduced by Floer \cite{floer:fixed} in the context of Hamiltonian Floer homology. The author employed the notion in the Lagrangian context for the pair $(\phi_H^1(L),L)$ of compact Lagrangian…

We classify all the $n$-component links in the $3$-sphere that bound a Thurston norm minimizing Seifert surface $\Sigma$ with Euler characteristic $\chi(\Sigma)=n-2$ and that are nearly fibered, which means that their rank of the maximal…

Two link diagrams on compact surfaces are strongly equivalent if they are related by Reidemeister moves and orientation preserving homeomorphisms of the surfaces. They are stably equivalent if they are related by the two previous operations…

A categorification of a polynomial link invariant is an homological invariant which contains the polynomial one as its graded Euler characteristic. This field has been initiated by Khovanov categorification of the Jones polynomial. Later,…

Let $\Gamma$ be a discrete subgroup of a unimodular locally compact group $G$. In Math. Ann. 388, 4251-4305 (2024), it was shown that the $L_p$ norm of a Fourier multiplier $m$ on $\Gamma$ can be bounded locally by its $L_p$-norm on $G$,…

We show that there exists a $\mathbb{Z}^\infty$-summand in the subgroup of the knot concordance group generated by knots with trivial Alexander polynomial. To this end we use the invariant Upsilon $\Upsilon$ recently introduced by…

We introduce a 4-dimensional analogue of the rational Seifert genus of a knot $K\subset Y$, which we call the rational slice genus, that measures the complexity of a homology class in $H_2(Y\times [0,1],K;\mathbb{Q})$. Our main theorem is a…

We give new obstructions to the module structures arising in Heegaard Floer homology. As a corollary, we characterize the possible modules arising as the Heegaard Floer homology of an integer homology sphere with one-dimensional reduced…

We introduce a generalization of the Ozsv\'ath-Szab\'o $\tau$-invariant to links by studying a filtered version of link grid homology. We prove that this invariant remains unchanged under strong concordance and we show that it produces a…

We equip the basic local crossing bimodules in Ozsv\'ath-Szab\'o's theory of bordered knot Floer homology with the structure of 1-morphisms of 2-representations, categorifying the $U_q(\mathfrak{gl}(1|1)^+)$-intertwining property of the…

In this paper we introduce a chain complex $C_{1 \pm 1}(D)$ where D is a plat braid diagram for a knot K. This complex is inspired by knot Floer homology, but it the construction is purely algebraic. It is constructed as an oriented cube of…

For an adiscal or monotone regular coisotropic submanifold $N$ of a symplectic manifold I define its Floer homology to be the Floer homology of a certain Lagrangian embedding of $N$. Given a Hamiltonian isotopy $\phi=(\phi^t)$ and a…

We introduce and study in detail an invariant of (1,1) tangles. This invariant, derived from a family of four dimensional representations of the quantum superalgebra U_q[gl(2|1)], will be referred to as the Links-Gould invariant. We find…

A. Casson defined an intersection number invariant which can be roughly thought of as the number of conjugacy classes of irreducible representations of $\pi_1(Y)$ into $SU(2)$ counted with signs, where $Y$ is an oriented integral homology…