Linear independence in the rational homology cobordism group
arXiv:1803.07931 · doi:10.1017/S1474748019000434
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.
12 pages. To appear in J. Inst. Math. Jussieu