Linear independence in the rational homology cobordism group

Marco Golla (1, 2) , Kyle Larson

1 CNRS - Centre National de la Recherche Scientifique
2 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Domaines: Topologie géométrique [math.GT]

Marco Golla, Kyle Larson. Linear independence in the rational homology cobordism group. Journal of the Institute of Mathematics of Jussieu, 2021, 20 (3), pp.989--1000. ⟨10.1017/S1474748019000434⟩. ⟨hal-02182676⟩