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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A lower bound for the double slice genus


Author: Wenzhao Chen
Journal: Trans. Amer. Math. Soc. 374 (2021), 2541-2558
MSC (2020): Primary 57K10, 57K31
DOI: https://doi.org/10.1090/tran/8191
Published electronically: February 2, 2021
MathSciNet review: 4223025
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Abstract: In this paper, we develop a lower bound for the double slice genus of a knot using Casson-Gordon invariants. As an application, we show that the double slice genus can be arbitrarily larger than twice the slice genus. As an analogue to the double slice genus, we also define the superslice genus of a knot, and give both an upper bound and a lower bound in the topological category.


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Additional Information

Wenzhao Chen
Affiliation: Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
MR Author ID: 1309566
Email: chenwenz@msu.edu

Received by editor(s): January 24, 2020
Received by editor(s) in revised form: April 30, 2020, and May 2, 2020
Published electronically: February 2, 2021
Additional Notes: The author is grateful to the Max Planck Institute for Mathematics in Bonn for its hospitality and financial support.
Article copyright: © Copyright 2021 American Mathematical Society