Contact structures, CR Yamabe invariant, and connected sum

Dietrich, Gautier

doi:10.1090/tran/8081

Contact structures, CR Yamabe invariant, and connected sum
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Trans. Amer. Math. Soc. 374 (2021), 881-897 Request permission

Abstract:

We propose a global invariant $\sigma _c$ for contact manifolds which admit a strictly pseudoconvex CR structure, analogous to the Yamabe invariant $\sigma$. We prove that this invariant is non-decreasing under handle attaching and under connected sum. We then give a lower bound on $\sigma _c$ in a particular case.

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