LINEAR INDEPENDENCE IN THE RATIONAL HOMOLOGY COBORDISM GROUP. (28th May 2021)

• Record Type: Journal Article
• Authors: Golla, Marco; Larson, Kyle
• Is Part Of: Journal of the Institute of Mathematics of Jussieu. Volume 20:Number 3(2021)
• Page Start: 989
• Page End: 1000
• Publication Date: 2021-05-28
• Subjects: homology cobordism, -- knot concordance, -- correction terms; 57M27, -- 57M25; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S1474748019000434
• Languages: English
• ISSNs: 1474-7480

Abstract

Abstract: We give simple homological conditions for a rational homology 3-sphere $Y$ to have infinite order in the rational homology cobordism group $\unicode[STIX]{x1D6E9}_{\mathbb{Q}}^{3}$, 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.