KNOT CONCORDANCE IN HOMOLOGY COBORDISMS
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