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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Contact structures, CR Yamabe invariant, and connected sum


Author: Gautier Dietrich
Journal: Trans. Amer. Math. Soc. 374 (2021), 881-897
MSC (2020): Primary 53D10
DOI: https://doi.org/10.1090/tran/8081
Published electronically: November 18, 2020
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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.


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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

DOI: https://doi.org/10.1090/tran/8081
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)
Article copyright: © Copyright 2020 American Mathematical Society