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Two knots are homology concordant if they are smoothly concordant in ahomology cobordism. The group $\hat{\mathcal{C}}_{\mathbb{Z}}$ (resp.$\mathcal{C}_{\mathbb{Z}}$) was previously defined as the set of knots inhomology spheres that bounds homology balls (resp. in $S^3$), modulo homologyconcordance. We prove $\hat{\mathcal{C}}_{\mathbb{Z}} /\mathcal{C}_{\mathbb{Z}}$ contains a $\mathbb{Z}^{\infty}$ subgroup. Weconstruct our family of examples by applying the filtered mapping cone formulato $L$--space knots, and prove linear independence with the help of theconnected knot complex.

Homology concordance and an infinite rank free subgroup