A reconstruction lemma for enhanced bypass sequences

Abstract

In the appendix of [LSV26], the authors produce an invariant for contact structures on $\Sigma \times [0,1]$. In this paper, we prove a result announced there which states that this is in-fact a full invariant. As an application, we provide an independent proof of Eliashbergs theorem and show that various construction methods for contact structures are equivalent.

14 pages, 7 Figures, Comments are welcome!