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Equivariant cobordisms between freely periodic knots

Part of: Differential topology Low-dimensional topology

Published online by Cambridge University Press:  22 June 2022

Keegan Boyle Open the ORCID record for Keegan Boyle [Opens in a new window]  and
Jeffrey Musyt
Keegan Boyle*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC, Canada
Jeffrey Musyt
Affiliation:
Department of Mathematics and Statistics, Slippery Rock University, Slippery Rock, PA, USA e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

We consider free symmetries on cobordisms between knots, which is equivalent to cobordisms between knots in lens spaces. We classify which freely periodic knots bound equivariant surfaces in the 4-ball in terms of corresponding homology classes in lens spaces. We give a numerical condition determining the free periods for which torus knots bound equivariant surfaces in the 4-ball.

Keywords

Knot theoryequivariant cobordismfreely periodic knots

MSC classification

Secondary: 57R85: Equivariant cobordism 57M60: Group actions in low dimensions
Type
Article
Information
Canadian Mathematical Bulletin , Volume 66 , Issue 2 , June 2023 , pp. 450 - 457
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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