Algebraic and Giroux torsion in higher-dimensional contact manifolds

Moreno, Agustin

doi:10.2140/agt.2024.24.3199

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Algebraic and Giroux torsion in higher-dimensional contact manifolds

Agustin Moreno

Algebraic & Geometric Topology 24 (2024) 3199–3234

DOI: 10.2140/agt.2024.24.3199

Abstract

We construct examples in any odd dimension of contact manifolds with finite and nonzero algebraic torsion (in the sense of Latschev and Wendl (2011)), which are therefore tight and do not admit strong symplectic fillings. We prove that Giroux torsion implies algebraic $1$ –torsion in any odd dimension, which proves a conjecture of Massot, Niederkrüger and Wendl (2013). These results are part of the author’s PhD thesis.

Keywords

contact manifolds, symplectic manifolds, symplectic field theory, holomorphic curves

Mathematical Subject Classification

Primary: 53D42, 57R17

References

Publication

Received: 14 September 2020

Revised: 6 January 2023

Accepted: 10 January 2023

Published: 7 October 2024

Authors

Agustin Moreno
Institute for Advanced Study Princeton, NJ United States

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Volume 24, issue 6 (2024)