Critical Heegaard surfaces obtained by amalgamation

2011/09/18 by Jung Hoon Lee, Lee, Jung Hoon · 1 citation
Mathematics · #57M50 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M50

paper · pdf · doi:10.48550/arxiv.1109.3862

7 pages, 3 figures

arxiv created 2011/09/18 · arxiv updated 2011/09/20

Abstract

Critical surfaces are defined by Bachman as topological index 2 surfaces, generalizing incompressible surfaces and strongly irreducible surfaces. In this paper we give a condition to obtain critical Heegaard surfaces by amalgamation. As a special case, we obtain critical Heegaard surfaces by boundary stabilization. It gives critical Heegaard surfaces of non-minimal genus, for 3-manifolds which do not admit distinct Heegaard splittings (up to isotopy).

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• Critical Heegaard surfaces obtained by self-amalgamation

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