Two-solvable and two-bipolar knots with large four-genera

Cha, Jae Choon; Miller, Allison N.; Powell, Mark

doi:10.4310/mrl.2021.v28.n2.a2

Two-solvable and two-bipolar knots with large four-genera

Cha, Jae Choon; Miller, Allison N.; Powell, Mark

Authors

Jae Choon Cha

Allison N. Miller

Mark Powell

Abstract

For every integer g, we construct a 2-solvable and 2-bipolar knot whose topological 4-genus is greater than g. Note that 2-solvable knots are in particular algebraically slice and have vanishing Casson–Gordon obstructions. Similarly all known smooth 4-genus bounds from gauge theory and Floer homology vanish for 2-bipolar knots. Moreover, our knots bound smoothly embedded height four gropes in D4, an a priori stronger condition than being 2-solvable. We use new lower bounds for the 4-genus arising from L(2)-signature defects associated to meta-metabelian representations of the fundamental group.

Citation

Cha, J. C., Miller, A. N., & Powell, M. (2021). Two-solvable and two-bipolar knots with large four-genera. Mathematical Research Letters, 28(2), 331-382. https://doi.org/10.4310/mrl.2021.v28.n2.a2

Journal Article Type	Article
Acceptance Date	Mar 20, 2020
Online Publication Date	Mar 13, 2021
Publication Date	2021
Deposit Date	Mar 29, 2020
Publicly Available Date	May 11, 2020
Journal	Mathematical Research Letters
Print ISSN	1073-2780
Electronic ISSN	1945-001X
Publisher	International Press
Peer Reviewed	Peer Reviewed
Volume	28
Issue	2
Pages	331-382
DOI	https://doi.org/10.4310/mrl.2021.v28.n2.a2
Related Public URLs	https://arxiv.org/abs/1901.02060