Two constructions of virtually contact structures

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.

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KW is supported by the SFB 878 “Groups, Geometry and Actions.” KZ is partially supported by the SFB/TRR 191, “Symplectic Structures in Geometry, Algebra and Dynamics,” and by DFG grant ZE 992/1-1.

Received 10 December 2016

Accepted 10 November 2017

Published 18 July 2018