Journal Article (Journal Article)

Let CbZ 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 C to CbZ 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.

Full Text

Duke Authors

Cited Authors

  • Hom, J; Levine, AS; Lidman, T

Published Date

  • October 15, 2022

Published In

Volume / Issue

  • 171 / 15

Start / End Page

  • 3089 - 3131

International Standard Serial Number (ISSN)

  • 0012-7094

Digital Object Identifier (DOI)

  • 10.1215/00127094-2021-0110

Citation Source

  • Scopus