On Legendrian products and twist spuns

Dimitroglou Rizell, Georgios; Golovko, Roman

doi:10.2140/agt.2021.21.665

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On Legendrian products and twist spuns

Georgios Dimitroglou Rizell and Roman Golovko

Algebraic & Geometric Topology 21 (2021) 665–695

DOI: 10.2140/agt.2021.21.665

Abstract

The Legendrian product of two Legendrian knots, as defined by Lambert-Cole, is a Legendrian torus. We show that this Legendrian torus is a twist spun whenever one of the Legendrian knot components is sufficiently large. We then study examples of Legendrian products which are not Legendrian isotopic to twist spuns. In order to do this, we prove a few structural results on the bilinearised Legendrian contact homology and augmentation variety of a twist spun. In addition, we show that the threefold Bohr–Sommerfeld covers of the Clifford torus and Chekanov torus are not twist spuns.

Keywords

Legendrian product, twist spun, looseness, fillability

Mathematical Subject Classification 2010

Primary: 53D12

Secondary: 53D42

References

Publication

Received: 15 July 2019

Revised: 7 June 2020

Accepted: 24 June 2020

Published: 25 April 2021

Authors

Georgios Dimitroglou Rizell
Department of Mathematics Uppsala University Uppsala Sweden
http://www.dimitroglou.name
Roman Golovko
Faculty of Mathematics and Physics Charles University Praha Czech Republic
https://sites.google.com/site/ragolovko/

Volume 21, issue 2 (2021)