Floer homology, twist coefficients, and capping off

TL;DR

This paper uses Heegaard Floer homology to analyze how fractional Dehn twist coefficients change when capping off boundary components in open book decompositions, and applies these results to study Floer homology of branched covers.

Contribution

It introduces a method to constrain the behavior of fractional Dehn twist coefficients after capping off using Heegaard Floer homology, linking boundary behavior to Floer invariants.

Findings

Constraints on fractional Dehn twist coefficients after capping off

Relationships between boundary twists and Floer homology of branched covers

Insights into the Floer homology of cyclic branched covers over fibered links

Abstract

For an open book decomposition $(S,\phi)$, the fractional Dehn twist coefficients are rational numbers measuring the amount that the monodromy $\phi$ twists the surface $S$ near each boundary component. In general, the twist coefficients do not behave nicely under the operation of capping off a boundary component. The goal of this paper is to use Heegaard Floer homology to constrain the behavior of the fractional Dehn twist coefficients after capping off. We also use our results about fractional Dehn twists to study the Floer homology of cyclic branched covers over fibered two-component links.