Khovanov homology and exotic surfaces in the 4-ball-Reference-Cited by-同舟云学术

Khovanov homology and exotic surfaces in the 4-ball

Published:2024-03-20 Issue:0 Volume:0 Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Hayden Kyle¹,Sundberg Isaac²

Affiliation:

1. Department of Mathematics and Computer Science , 67206 Rutgers University , Newark , NJ 07102 , USA

2. 28264 Max Planck Institut für Mathematik , 53111 Bonn , Germany

Abstract

Abstract We show that the cobordism maps on Khovanov homology can distinguish smooth surfaces in the 4-ball that are exotically knotted (i.e., isotopic through ambient homeomorphisms but not ambient diffeomorphisms). We develop new techniques for distinguishing cobordism maps on Khovanov homology, drawing on knot symmetries and braid factorizations. We also show that Plamenevskaya’s transverse invariant in Khovanov homology is preserved by maps induced by positive ascending cobordisms.

Funder

National Science Foundation

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2024-0001/pdf

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