Branched covers and rational homology balls

Livingston, Charles

doi:10.2140/agt.2024.24.587

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Branched covers and rational homology balls

Charles Livingston

Algebraic & Geometric Topology 24 (2024) 587–594

DOI: 10.2140/agt.2024.24.587

Abstract

The concordance group of knots in $S^{3}$ contains a subgroup isomorphic to ${(ℤ_{2})}^{\infty}$ , each element of which is represented by a knot $K$ with the property that, for every $n > 0$ , the $n$ –fold cyclic cover of $S^{3}$ 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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Volume 24, issue 1 (2024)