On naturality of the Ozsvath-Szabo contact invariant

TL;DR

This paper explores the properties of the Ozsvath-Szabo contact invariant, establishing its functoriality, basepoint independence, and behavior under Stein cobordisms, thus clarifying its foundational aspects in contact topology.

Contribution

It provides new proofs and clarifications on the functoriality and basepoint dependence of the Ozsvath-Szabo contact invariant, including its strong functoriality under Stein cobordisms.

Findings

Invariant is independent of the basepoint.

Invariant is functorial under contactomorphisms.

Invariant is strongly functorial under Stein cobordisms.

Abstract

We discuss functoriality properties of the Ozsvath-Szabo contact invariant, and expose a number of results which seemed destined for folklore. We clarify the (in)dependence of the invariant on the basepoint, prove that it is functorial with respect to contactomorphisms, and show that it is strongly functorial under Stein cobordisms.