#### Volume 21, issue 1 (2021)

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On symplectic fillings of virtually overtwisted torus bundles

### Austin Christian

Algebraic & Geometric Topology 21 (2021) 469–505
##### 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.

##### Keywords
symplectic filling, contact manifold, virtually overtwisted
Primary: 53D10
Secondary: 53D05
##### 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