Homology concordance and an infinite rank free subgroup

摘要

Two knots are homology concordant if they are smoothly concordant in a homology cobordism. The group CZ (respectively, CZ) was previously defined as the set of knots in homology spheres that bounds homology balls (respectively, in S3), modulo homology concordance. We prove CZ/CZ contains a Z infinity 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.