Some non-trivial examples of the Baldwin-Ozsv\'ath-Szab\'o twisted spectral sequence and Heegaard-Floer homology of branched double covers

TL;DR

This paper provides complex calculations of Baldwin-Ozsváth-Szabó cohomology for links and explores their implications for Heegaard-Floer homology of branched double covers, advancing understanding in low-dimensional topology.

Contribution

It introduces new non-trivial examples of the Baldwin-Ozsváth-Szabó spectral sequence and applies these to compute Heegaard-Floer homology of branched double covers.

Findings

Computed specific Baldwin-Ozsváth-Szabó cohomology examples

Linked cohomology calculations to Heegaard-Floer homology results

Enhanced understanding of spectral sequence applications in topology

Abstract

We present some non-trivial calculations of Baldwin-Ozsv\'{a}th-Szab\'{o} cohomology of links, and applications to Heegaard-Floer homology of branched double covers.