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On Legendrian products
and twist spuns
Georgios Dimitroglou Rizell and Roman Golovko |
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Algebraic & Geometric Topology 21 (2021) 665–695
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Abstract |
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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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Keywords
Legendrian product, twist spun, looseness, fillability
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Mathematical Subject Classification 2010
Primary: 53D12
Secondary: 53D42
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References |
Publication
Received: 15 July 2019
Revised: 7 June 2020
Accepted: 24 June 2020
Published: 25 April 2021
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Authors |
| Georgios Dimitroglou Rizell | |
| Department of Mathematics Uppsala University Uppsala Sweden |
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| http://www.dimitroglou.name | |
| Roman Golovko | |
| Faculty of Mathematics and
Physics Charles University Praha Czech Republic |
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| https://sites.google.com/site/ragolovko/ | |
