On the minimal number of translated points in contact lens spaces

Allais, Simon

doi:10.1090/proc/15863

On the minimal number of translated points in contact lens spaces
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by Simon Allais

Proc. Amer. Math. Soc. 150 (2022), 2685-2693

DOI: https://doi.org/10.1090/proc/15863

Published electronically: March 7, 2022

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Abstract:

In this article, we prove that every contactomorphism of any standard contact lens space of dimension $2n-1$ that is contact-isotopic to the identity has at least $2n$ translated points with respect to the standard contact form. This sharp lower bound refines a result of Granja-Karshon-Pabiniak-Sandon [Givental’s non-linear Maslov index on lens spaces arXiv:1704.05827, 2017] and confirms a conjecture of Sandon.

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