PL-Genus of surfaces in homology balls
| Autor: | Jennifer Hom, Matthew Stoffregen, Hugo Zhou |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Forum of Mathematics, Sigma, Vol 12 (2024) |
| Druh dokumentu: | article |
| ISSN: | 2050-5094 |
| DOI: | 10.1017/fms.2023.126 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|