Volume 21, issue 2 (2021)

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On Legendrian products and twist spuns

Georgios Dimitroglou Rizell and Roman Golovko

Algebraic & Geometric Topology 21 (2021) 665–695

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.

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Legendrian product, twist spun, looseness, fillability
Mathematical Subject Classification 2010
Primary: 53D12
Secondary: 53D42
Received: 15 July 2019
Revised: 7 June 2020
Accepted: 24 June 2020
Published: 25 April 2021
Georgios Dimitroglou Rizell
Department of Mathematics
Uppsala University
Roman Golovko
Faculty of Mathematics and Physics
Charles University
Czech Republic