February 2024 A Note on the Concordance Z-Genus
Allison N. Miller, JungHwan Park
Michigan Math. J. 74(1): 73-83 (February 2024). DOI: 10.1307/mmj/20216070

Abstract

We show that the difference between the topological 4-genus of a knot and the minimal genus of a surface bounded by that knot that can be decomposed into a smooth concordance followed by an algebraically simple locally flat surface can be arbitrarily large. This extends work of Hedden, Livingston, and Ruberman showing that there are topologically slice knots which are not smoothly concordant to any knot with trivial Alexander polynomial.

Citation

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Allison N. Miller. JungHwan Park. "A Note on the Concordance Z-Genus." Michigan Math. J. 74 (1) 73 - 83, February 2024. https://doi.org/10.1307/mmj/20216070

Information

Received: 14 April 2021; Revised: 28 June 2021; Published: February 2024
First available in Project Euclid: 25 February 2024

MathSciNet: MR4718492
Digital Object Identifier: 10.1307/mmj/20216070

Keywords: 57K10 , 57K18 , 57K40 , 57N70

Rights: Copyright © 2024 The University of Michigan

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Vol.74 • No. 1 • February 2024
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