On symplectic fillings of virtually overtwisted torus bundles

Christian, Austin

doi:10.2140/agt.2021.21.469

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On symplectic fillings of virtually overtwisted torus bundles

Austin Christian

Algebraic & Geometric Topology 21 (2021) 469–505

DOI: 10.2140/agt.2021.21.469

Abstract

We use Menke’s JSJ-type decomposition theorem for symplectic fillings to reduce the classification of strong and exact symplectic fillings of virtually overtwisted contact structures on torus bundles to the same problem for tight lens spaces. For virtually overtwisted structures on elliptic or parabolic torus bundles, this gives a complete classification. For virtually overtwisted structures on hyperbolic torus bundles, we show that every strong or exact filling arises from a filling of a tight lens space via round symplectic $1$ –handle attachment, and we give a condition under which distinct tight lens space fillings yield the same torus bundle filling.

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Keywords

symplectic filling, contact manifold, virtually overtwisted

Mathematical Subject Classification 2010

Primary: 53D10

Secondary: 53D05

References

Publication

Received: 10 October 2019

Revised: 23 January 2020

Accepted: 19 March 2020

Published: 25 February 2021

Authors

Austin Christian
Department of Mathematics University of California, Los Angeles Los Angeles, CA United States
https://www.math.ucla.edu/~archristian

Volume 21, issue 1 (2021)