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Branched covers and rational homology balls

Charles Livingston

Algebraic & Geometric Topology 24 (2024) 587–594
Abstract

The concordance group of knots in S3 contains a subgroup isomorphic to (2), each element of which is represented by a knot K with the property that, for every n > 0, the n–fold cyclic cover of S3 branched over K bounds a rational homology ball. This implies that the kernel of the canonical homomorphism from the knot concordance group to the infinite direct sum of rational homology cobordism groups (defined via prime-power branched covers) contains an infinitely generated two-torsion subgroup.

Keywords
branched cover, knot, rational homology ball
Mathematical Subject Classification
Primary: 57K10, 57M12
References
Publication
Received: 17 May 2022
Revised: 3 August 2022
Accepted: 25 August 2022
Published: 18 March 2024
Authors
Charles Livingston
Department of Mathematics
Indiana University
Bloomington, IN
United States

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