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

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

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.

• Item Type: Articles
• Additional Information: The first author was partly supported by NRF grant 2019R1A3B206 7839.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Powell, Dr Mark
• Authors: Cha, J. C., Miller, A. N., and Powell, M.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Mathematical Research Letters
• Publisher: International Press
• ISSN: 1073-2780
• ISSN (Online): 1945-001X
• Published Online: 13 May 2021
• Copyright Holders: Copyright © International Press 2021
• First Published: First published in Mathematical Research Letters 28(2): 331-382
• Publisher Policy: Reproduced in accordance with the publisher copyright policy