Homology concordance and an infinite rank free subgroup

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Abstract: Two knots are homology concordant if they are smoothly concordant in a homology cobordism. The group

h a t {m a t h c a l C}_{m a t h b b Z}

(resp.

m a t h c a l C_{m a t h b b Z}

) was previously defined as the set of knots in homology spheres that bounds homology balls (resp. in

S^{3}

), modulo homology concordance. We prove

h a t {m a t h c a l C}_{m a t h b b Z} / m a t h c a l C_{m a t h b b Z}

contains a

m a t h b b Z^{i n f t y}

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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