Miller, A. N. and Powell, M. (2023) Strongly invertible knots, equivariant slice genera, and an equivariant algebraic concordance group. Journal of the London Mathematical Society, 107(6), pp. 2025-2053. (doi: 10.1112/jlms.12732)
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Abstract
We use the Blanchfield form to obtain a lower bound on the equivariant slice genus of a strongly invertible knot. For our main application, let K be a genus one strongly invertible slice knot with nontrivial Alexander polynomial. We show that the equivariant slice genus of an equivariant connected sum #^n K is at least n/4. We also formulate an equivariant algebraic concordance group, and show that the kernel of the forgetful map to the classical algebraic concordance group is infinite rank.
| Item Type: | Articles |
|---|---|
| Additional Information: | MP was partially supported by EPSRC New Investigator grant EP/T028335/1 and EPSRC New Horizons grant EP/V04821X/1. |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Powell, Professor Mark |
| Authors: | 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: | Journal of the London Mathematical Society |
| Publisher: | Wiley |
| ISSN: | 0024-6107 |
| ISSN (Online): | 1469-7750 |
| Published Online: | 05 March 2023 |
| Copyright Holders: | Copyright © 2023 The Authors |
| First Published: | First published in Journal of the London Mathematical Society 107(6):2025-2053 |
| Publisher Policy: | Reproduced under a Creative Commons license |
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