Geodesic
PL-Genus of surfaces in homology balls
Forum of Mathematics, Sigma, Tome 12 (2024)

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We consider manifold-knot pairs $(Y,K)$, where Y is a homology 3-sphere that bounds a homology 4-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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     author = {Jennifer Hom and Matthew Stoffregen and Hugo Zhou},
     title = {PL-Genus of surfaces in homology balls},
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Jennifer Hom; Matthew Stoffregen; Hugo Zhou. PL-Genus of surfaces in homology balls. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2023.126

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