Homology concordance and an infinite rank free subgroup

2020/09/10 by Hugo Zhou, Zhou, Hugo · 1 citation
Mathematics · Medicine · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Botulinum Toxin and Related Neurological Disorders

paper · pdf · doi:10.48550/arxiv.2009.05145

Abstract

Two knots are homology concordant if they are smoothly concordant in a homology cobordism. The group C_ℤ (resp. C_ℤ) was previously defined as the set of knots in homology spheres that bounds homology balls (resp. in S³), modulo homology concordance. We prove C_ℤ / C_ℤ contains a ℤ^∞ subgroup. We construct our family of examples by applying the filtered mapping cone formula to L--space knots, and prove linear independence with the help of the connected knot complex.

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