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2021 On Legendrian products and twist spuns
Georgios Dimitroglou Rizell, Roman Golovko
Algebr. Geom. Topol. 21(2): 665-695 (2021). 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.

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Georgios Dimitroglou Rizell. Roman Golovko. "On Legendrian products and twist spuns." Algebr. Geom. Topol. 21 (2) 665 - 695, 2021. https://doi.org/10.2140/agt.2021.21.665

Information

Received: 15 July 2019; Revised: 7 June 2020; Accepted: 24 June 2020; Published: 2021
First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.2140/agt.2021.21.665

Subjects:
Primary: 53D12
Secondary: 53D42

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.21 • No. 2 • 2021
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