Branched covers and rational homology balls

Charles Livingston

doi:10.2140/agt.2024.24.587

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arXiv · 2202.06713

Branched covers and rational homology balls

Charles Livingston

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Abstract

The concordance group of knots in the three-sphere contains an infinite subgroup generated by elements of order two, each one 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.

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Charles Livingston. 2022-02-14. Branched covers and rational homology balls. https://doi.org/10.2140/agt.2024.24.587

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