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

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

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
• Public URL: https://durham-repository.worktribe.com/output/1273876
• Related Public URLs: https://arxiv.org/abs/1901.02060