The embedded contact homology of sutured solid tori

TL;DR

This paper computes the relative embedded contact homology and related invariants for sutured solid tori with multiple parallel sutures, advancing understanding of contact topology in these 3-manifolds.

Contribution

It provides explicit calculations of embedded contact homology and related invariants for sutured solid tori with multiple sutures, a case previously not fully understood.

Findings

Explicit formulas for embedded contact homology of sutured solid tori

Calculation of contact and cylindrical contact homology in this setting

Extension of contact topological invariants to sutured manifolds

Abstract

We calculate the relative versions of embedded contact homology, contact homology and cylindrical contact homology of the sutured solid torus $(S^1\times D^2,\Gamma)$, where $\Gamma$ consists of $2n$ parallel longitudinal sutures.