Many Haken Heegaard splittings

Alessandro Sisto*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We give a simple criterion for a Heegaard splitting to yield a Haken manifold. As a consequence, we construct many Haken manifolds, in particular homology spheres, with prescribed properties, namely Heegaard genus, Heegaard distance and Casson invariant. Along the way we give simpler and shorter proofs of the existence of splittings with specified Heegaard distance, originally proven by Ido-Jang-Kobayashi, of the existence of hyperbolic manifolds with prescribed Casson invariant, originally due to Lubotzky-Maher-Wu, and of a result about subsurface projections of disc sets (for which we even get better constants), originally due to Masur-Schleimer.

Original languageEnglish
Pages (from-to)357-369
Number of pages13
JournalJournal of Topology and Analysis
Issue number2
Publication statusPublished - 1 Jun 2020


  • Casson invariant
  • Haken manifold
  • Heegaard splitting
  • Incompressible surface

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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