Effective finiteness of irreducible Heegaard splittings of non-Haken 3-manifolds

Tobias Holck Colding, David Gabai

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

The main result is a short effective proof of Tao Li's theorem that a closed non-Haken hyperbolic 3-manifold N has at most finitely many irreducible Heegaard splittings. Along the way we show that N has finitely many branched surfaces of pinched negative sectional curvature carrying all closed index-≤ 1 minimal surfaces. This effective result, together with the sequel with Daniel Ketover, solves the classification problem for Heegaard splittings of non-Haken hyperbolic 3-manifolds.

Original languageEnglish (US)
Pages (from-to)2793-2832
Number of pages40
JournalDuke Mathematical Journal
Volume167
Issue number15
DOIs
StatePublished - Oct 1 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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