Genus One Cobordisms Between Torus Knots-Reference-Cited by-同舟云学术

Genus One Cobordisms Between Torus Knots

Published:2020-03-04 Issue:1 Volume:2021 Page:521-548
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Feller Peter¹,Park JungHwan²

Affiliation:

1. Eidgenössische Technische Hochschule Zürich, Rämistrasse 101, 8092 Zürich, Switzerland

2. School of Mathematics, Georgia Institute of Technology, Atlanta, 30332-0160 GA, USA

Abstract

Abstract We determine the pairs of torus knots that have a genus one cobordism between them, with one notable exception. This is done by combining obstructions using $\nu ^+$ from the Heegaard Floer knot complex and explicit constructions of cobordisms. As an application, we determine the pairs of torus knots related by a single crossing change. Also, we determine the pairs of Thurston–Bennequin number maximizing Legendrian torus knots that have a genus one exact Lagrangian cobordism, with one exception.

Funder

Swiss National Science Foundation

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/1/521/36348369/rnaa027.pdf

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