Two-solvable and two-bipolar knots with large four-genera
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SCOPUS
- Title
- Two-solvable and two-bipolar knots with large four-genera
- Authors
- Cha, Jae Choon; Miller, Allison N.; Powell, Mark
- Date Issued
- 2021-05
- Publisher
- INT PRESS BOSTON, INC
- 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 D-4, 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.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/106668
- DOI
- 10.4310/MRL.2021.v28.n2.a2
- ISSN
- 1073-2780
- Article Type
- Article
- Citation
- MATHEMATICAL RESEARCH LETTERS, vol. 28, no. 2, page. 331 - 382, 2021-05
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