Linear independence in the rational homology cobordism group

Marco Golla; Kyle Larson

doi:10.1017/s1474748019000434

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arXiv · 1803.07931

Linear independence in the rational homology cobordism group

Marco Golla·Kyle Larson

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Abstract

We give simple homological conditions for a rational homology 3-sphere Y to have infinite order in the rational homology cobordism group, and for a collection of rational homology spheres to be linearly independent. These translate immediately to statements about knot concordance when Y is the branched double cover of a knot, recovering some results of Livingston and Naik. The statements depend only on the homology groups of the 3-manifolds, but are proven through an analysis of correction terms and their behavior under connected sums.

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Marco Golla, Kyle Larson. 2018-03-21. Linear independence in the rational homology cobordism group. https://doi.org/10.1017/s1474748019000434

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