Contact categories of disks

Abstract

In the first part of the paper we associate a pre-additive category $\mathcal{C}(\Sigma )$ to a closed oriented surface $\Sigma$, called the {\em contact category} and constructed from contact structures on $\Sigma \times [0,1]$. There are also $\mathcal{C}(\Sigma ,F)$, where $\Sigma$ is a compact oriented surface with boundary and $F\subset \partial \Sigma$ is a finite oriented set of points which bounds a submanifold of $\partial \Sigma$, and universal covers $\tilde{\mathcal{C}}(\Sigma )$ and $\tilde{\mathcal{C}}(\Sigma ,F)$ of $\mathcal{C}(\Sigma )$ and $\mathcal{C}(\Sigma ,F)$. In the second part of the paper we prove that the universal cover of the contact category of a disk admits an embedding into its "triangulated envelope."

76 pages, 37 figures

References in corpus (2)

• Bordered Floer homology for sutured manifolds
• Formal Contact Categories

Cited by in corpus (2)

• Towards a categorical boson-fermion correspondence
• Formal Contact Categories