Knot concordance in homology cobordisms

Jennifer Hom; Adam Simon Levine; Tye Lidman

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arXiv · 1801.07770

Knot concordance in homology cobordisms

Jennifer Hom·Adam Simon Levine·Tye Lidman

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Abstract

Let $\widehat{\mathcal{C}}_{\mathbb{Z}}$ 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 $\mathcal{C}$ to $\widehat{\mathcal{C}}_{\mathbb{Z}}$ 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.

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Jennifer Hom, Adam Simon Levine, Tye Lidman. 2018-01-23. Knot concordance in homology cobordisms. https://arxiv.org/abs/1801.07770

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