Parity condition for irreducibility of Heegaard splittings

2008/12/01 by Jung Hoon Lee, Lee, Jung Hoon
Computer Science · Mathematics · #57N10 #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57N10 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0812.0225

The paper is totally rewritten. The title has been changed. 9 pages, 5 figures

openalex publication_date 2008/12/01 · arxiv created 2009/02/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Casson and Gordon gave the rectangle condition for strong irreducibility of Heegaard splittings [1]. We give a parity condition for irreducibility of Heegaard splittings of irreducible manifolds. As an application, we give examples of non-stabilized Heegaard splittings by doing a single Dehn twist.

Related

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• Heegaard splittings of the form H + nK
• Manifolds admitting both strongly irreducible and weakly reducible minimal genus Heegaard splittings
• Stabilizations of Reducible Heegaard Splittings
• How a strongly irreducible Heegaard splitting intersects a handlebody