PL-genus of surfaces in homology balls

Jennifer Hom; Matthew Stoffregen; Hugo Zhou

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arXiv · 2301.04729

PL-genus of surfaces in homology balls

Jennifer Hom·Matthew Stoffregen·Hugo Zhou

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Abstract

We consider manifold-knot pairs $(Y,K)$ where $Y$ is a homology sphere that bounds a homology ball. We show that the minimum genus of a PL surface $\Sigma$ in a homology ball $X$ such that $\partial (X, \Sigma) = (Y, K)$ can be arbitrarily large. Equivalently, the minimum genus of a surface cobordism in a homology cobordism from $(Y, K)$ to any knot in $S^3$ can be arbitrarily large. The proof relies on Heegaard Floer homology.

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Jennifer Hom, Matthew Stoffregen, Hugo Zhou. 2023-01-11. PL-genus of surfaces in homology balls. https://arxiv.org/abs/2301.04729

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