PL-Genus of surfaces in homology balls

DOI10.1017/FMS.2023.126arXiv2301.04729OpenAlexW4391232820MaRDI QIDQ6148466

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Publication date: 7 February 2024

Published in: (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/2301.04729

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