## Contact structures, CR Yamabe invariant, and connected sum

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## 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.## References

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## Additional Information

**Gautier Dietrich**- Affiliation: Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, CNRS, Case courrier 051, Place Eugène Bataillon, 34090 Montpellier, France; and Université Paul-Valéry Montpellier 3
- Email: gautier.dietrich@ac-toulouse.fr
- Received by editor(s): December 6, 2018
- Received by editor(s) in revised form: October 21, 2019, and December 17, 2019
- Published electronically: November 18, 2020
- Additional Notes: The author was supported in part by the grant ANR-17-CE40-0034 of the French National Research Agency ANR (project CCEM)
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**374**(2021), 881-897 - MSC (2020): Primary 53D10
- DOI: https://doi.org/10.1090/tran/8081
- MathSciNet review: 4196381