English

Linear independence in the rational homology cobordism group

Geometric Topology 2021-07-01 v2

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.

Keywords

Cite

@article{arxiv.1803.07931,
  title  = {Linear independence in the rational homology cobordism group},
  author = {Marco Golla and Kyle Larson},
  journal= {arXiv preprint arXiv:1803.07931},
  year   = {2021}
}

Comments

12 pages. To appear in J. Inst. Math. Jussieu