Given a grid presentation of a knot (or link) K in the three-sphere, we describe a Heegaard
diagram for the knot complement in which the Heegaard surface is a torus and all elementary …

We define $\operatorname {Pin}(2) $-equivariant Seiberg-Witten Floer homology for rational
homology $3 $-spheres equipped with a spin structure. The analogue of Frøyshov’s …

Link Floer homology is an invariant for links defined using a suitable version of Lagrangian
Floer homology. In an earlier paper, this invariant was given a combinatorial description with …

Using the conjugation symmetry on Heegaard Floer complexes, we define a 3 -manifold
invariant called involutive Heegaard Floer homology, which is meant to correspond to Z 4 -…

Quasi-alternating links are a natural generalization of alternating links. In this paper, we show
that quasi-alternating links are "homologically thin" for both Khovanov homology and knot …

Using Furuta’s idea of finite dimensional approximation in Seiberg–Witten theory, we refine
Seiberg–Witten Floer homology to obtain an invariant of homology 3–spheres which lives in …

The Knight Move Conjecture claims that the Khovanov homology of any knot decomposes
as direct sums of some “knight move” pairs and a single “pawn move” pair. This is true for …

Ozsváth and Szabó defined an analog of the Frøyshov invariant in the form of a correction
term for the grading in Heegaard Floer homology. Applying this to the double cover of the 3-…

The physical 3d ND 2 theory T ŒY was previously used to predict the existence of some 3-manifold
invariants yZa. q/that take the form of power series with integer coefficients, …

We prove a connected sum formula for involutive Heegaard Floer homology, and use it to
study the involutive correction terms of connected sums. In particular, we give an example of a …