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-sphere branched… (More)

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 Floer… (More)

We use finite dimensional approximation to construct from the Seiberg-Witten equations invariants of three-manifolds with b1 > 0 in the form of periodic pro-spectra. Their homology is the… (More)

Using Furuta’s idea of nite dimensional approximation in Seiberg{Witten theory, we re ne Seiberg{Witten Floer homology to obtain an invariant of homology 3{spheres which lives in the S1{equivariant… (More)

We define Pin(2)-equivariant Seiberg-Witten Floer homology for rational homology 3-spheres equipped with a spin structure. The analogue of Frøyshov’s correction term in this setting is an… (More)

Using the conjugation symmetry on Heegaard Floer complexes, we define a three-manifold invariant called involutive Heegaard Floer homology, which is meant to correspond to Z4-equivariant… (More)

We consider the models of distributed computation defined as subsets of the runs of the iterated immediate snapshot model. Given a task T and a model M, we provide topological conditions for T to be… (More)

In a previous paper, Sarkar and the third author gave a combinatorial description of the hat version of Heegaard Floer homology for three-manifolds. Given a cobordism between two three-manifolds,… (More)

For each positive integer n, Khovanov and Rozansky constructed an invariant of links in the form of a doubly-graded cohomology theory whose Euler characteristic is the sl(n) link polynomial. We use… (More)

Given a crossing in a planar diagram of a link in the three-sphere, we show that the knot Floer homologies of the link and its two resolutions at that crossing are related by an exact triangle. As a… (More)