Critical Heegaard surfaces obtained by amalgamation

Details Critical Heegaard surfaces obtained by amalgamation Critical Heegaard surfaces obtained by amalgamation

2011-09-18

arxiv.org/abs/1109.3862v1

Mathematics

Geometric Topology

7 pages, 3 figures

Scientific paper

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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