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correction terms

Journal of the Institute of Mathematics of Jussieu (1)

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1 results

LINEAR INDEPENDENCE IN THE RATIONAL HOMOLOGY COBORDISM GROUP
Part of
- Low-dimensional topology
Marco Golla, Kyle Larson
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 3 / May 2021

Published online by Cambridge University Press:

28 August 2019, pp. 989-1000

Print publication:

May 2021
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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.