Two constructions of virtually contact structures

TL;DR

This paper introduces new methods for constructing virtually contact structures, motivated by recent progress on the Weinstein conjecture, including a novel covering contact connected sum and structures on subcritical handle boundaries.

Contribution

It presents the first definition of covering contact connected sum for virtually contact manifolds and constructs such structures on boundaries of subcritical handle bodies.

Findings

Introduced covering contact connected sum for virtually contact manifolds

Constructed virtually contact structures on subcritical handle boundaries

Provides tools relevant for Weinstein conjecture research

Abstract

Motivated by recent developments in proving the Weinstein conjecture we introduce the notion of covering contact connected sum for virtually contact manifolds and construct virtually contact structures on boundaries of subcritical handle bodies.