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Involutions, knots, and Floer K-theory

Part of: Differential topology

Published online by Cambridge University Press:  16 December 2025

Hokuto Konno ,
Jin Miyazawa  and
Masaki Taniguchi Open the ORCID record for Masaki Taniguchi [Opens in a new window]
Hokuto Konno
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan konno@ms.u-tokyo.ac.jp
Jin Miyazawa
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan miyazawa.jin.5a@kyoto-u.ac.jp
Masaki Taniguchi
Affiliation:
Department of Mathematics, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan taniguchi.masaki.7m@kyoto-u.ac.jp
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Abstract

We establish a version of Seiberg–Witten Floer K-theory for knots, as well as a version of Seiberg–Witten Floer K-theory for 3-manifolds with involution. The main theorems are 10/8-type inequalities for knots and for involutions. The 10/8-inequality for knots yields numerous applications to knots, such as lower bounds on stabilizing numbers and relative genera. We also give obstructions to extending involutions on 3-manifolds to 4-manifolds, and detect non-smoothable involutions on 4-manifolds with boundary.

Keywords

involutionknot concordance invariantsreal 10/8-inequalityFloer K-cohomologyreal Floer homotopy type

MSC classification

Primary: 57R58: Floer homology

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Type
Research Article
Information
Compositio Mathematica , Volume 161 , Issue 11 , November 2025 , pp. 2852 - 2910
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© The Author(s), 2025. The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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