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A note on the four-dimensional clasp number of knots

Part of: Topological manifolds

Published online by Cambridge University Press:  16 July 2021

PETER FELLER  and
JUNGHWAN PARK
PETER FELLER
Affiliation:
ETH Zurich, Rämistrasse 101, 8092 Zurich, Switzerland e-mail: [email protected]
JUNGHWAN PARK
Affiliation:
KAIST, 291 Daehak-ro, Daejeon, 34141, South Korea e-mail: [email protected]
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Abstract

Among the knots that are the connected sum of two torus knots with cobordism distance 1, we characterise those that have 4-dimensional clasp number at least 2, and we show that their n-fold connected self-sum has 4-dimensional clasp number at least 2n. Our proof works in the topological category. To contrast this, we build a family of topologically slice knots for which the n-fold connected self-sum has 4-ball genus n and 4-dimensional clasp number at least 2n.

MSC classification

Primary: 57N70: Cobordism and concordance
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 173 , Issue 1 , July 2022 , pp. 213 - 226
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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