Related papers: Concordance maps in $HFK^{-}$

We show that a decorated knot concordance $C$ from $K$ to $K'$ induces a homomorphism $F_C$ on knot Floer homology that preserves the Alexander and Maslov gradings. Furthermore, it induces a morphism of the spectral sequences to…

We study the homology concordance group of knots in integer homology three-spheres which bound integer homology four-balls. Using knot Floer homology, we construct an infinite number of $\mathbb{Z}$-valued, linearly independent homology…

We study the maps induced on link Floer homology by elementary decorated link cobordisms. We compute these for births, deaths, stabilizations, and destabilizations, and show that saddle cobordisms can be computed in terms of maps in a…

If $K$ is a fibered knot in a closed, oriented $3$--manifold $Y$ with fiber $F$, and $\widehat{HFK}(Y,K,[F], g(F)-1;\mathbb Z/2\mathbb Z)$ has rank $r$, then the monodromy of $K$ is freely isotopic to a diffeomorphism with at most $r-1$…

Let $K$ be a null-homologous knot in a generalized L-space $Z$ with $b_1(Z)\le1$. Let $F$ be a Seifert surface of $K$ with genus $g$. We show that if $\widehat{HFK}(Z,K,[F],g)$ is supported in a single $\mathbb Z/2\mathbb Z$--grading, then…

Let $K$ denote a knot inside the homology sphere $Y$ and $K'$ denote a knot inside a homology sphere $L$-space. Let $X=Y(K,K')$ denote the 3-manifold obtained by splicing the complements of $K$ and $K'$. We show that…

It was recently proved by several authors that ribbon concordances induce injective maps in knot Floer homology, Khovanov homology, and the Heegaard Floer homology of the branched double cover. We give a simple proof of a similar statement…

We prove that, up to local equivalences, a suitable truncation of the involutive knot Floer homology of a knot in $S^3$ and the involutive bordered Heegaard Floer theory of its complement determine each other. In particular, given two knots…

We define an infinite family of linearly independent, integer-valued smooth concordance homomorphisms. Our homomorphisms are explicitly computable and rely on local equivalence classes of knot Floer complexes over the ring $\mathbb{F}[U,…

Ghosh-Sivek-Zentner constructed degree-1 maps from certain rational homology solid tori to the twisted $I$-bundle over the Klein bottle. We show that these maps yield rank inequalities for Heegaard Floer homology. To do so, we use…

Let $\widehat{\mathcal{C}}_{\mathbb{Z}}$ denote the group of knots in homology spheres that bound homology balls, modulo smooth concordance in homology cobordisms. Answering a question of Matsumoto, the second author previously showed that…

We apply the theory of "peculiar modules" for the Floer homology of 4-ended tangles developed by Zibrowius (specifically, the immersed curve interpretation of the tangle invariants) to compute the Knot Floer Homology ($\widehat{HFK}$) of…

Inspired by the $S^n$ colored version of Khovanov and Khovanov-Rozansky homology, we define a colored version of knot Floer homology by studying the colimit of a directed system of link Floer homology with infinite full twists.…

Knot Floer homology is a knot invariant defined using holomorphic curves. In more recent work, taking cues from bordered Floer homology,the authors described another knot invariant, called "bordered knot Floer homology", which has an…

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…

Consider an unknot $c$ in $S^3$ and a knot $K$ in ${S^3-N(c)}$. Twisting the knot $K$ along $c$, or equivalently applying $\frac{1}{m}$-surgery on $c$, produces a family of knots $\{K_m\}_{m \in \mathbb{Z}}$. We use bordered Floer homology…

To a nullhomologous knot $K$ in a 3-manifold $Y$, knot Floer homology associates a bigraded chain complex over $\mathbb{F}[U,V]$ as well as a collection of flip maps; we show that this data can be interpretted as a collection of decorated…

We prove that the map on knot Floer homology induced by a strongly homotopy-ribbon concordance is injective.

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 provide an affirmative answer by introducing a natural notion of cobordism between…

Given a transverse knot $K$ in a three dimensional contact manifold $(Y,\alpha)$, in [13] Colin, Ghiggini, Honda and Hutchings define a hat version of embedded contact homology for $K$, that we call $\widehat{ECK}(K,Y,\alpha)$, and…