Let denote the group of knots in homology spheres that bound homology balls, modulo smooth concordance in homology cobordisms. Answering a question of Matsumoto, the second author previously showed that the natural map from the smooth knot concordance group to is not surjective. Using tools from Heegaard Floer homology, we show that the cokernel of this map, which can be understood as the non-locally-flat piecewise-linear concordance group, is infinitely generated and contains elements of infinite order. In the appendix, we provide a careful proof that any piecewise-linear surface in a smooth 4-manifold can be isotoped to be smooth away from cone points.
"Knot concordance in homology cobordisms." Duke Math. J. 171 (15) 3089 - 3131, 15 October 2022. https://doi.org/10.1215/00127094-2021-0110