On boundary primitive manifolds and a theorem of Casson-Gordon

Details On boundary primitive manifolds and a theorem of Casson-Gordon On boundary primitive manifolds and a theorem of Casson-Gordon

2002-01-14

arxiv.org/abs/math/0201115v2

Mathematics

Geometric Topology

13 pages 3 figures. Will appear in Topology and its Applications

Scientific paper

In this paper it is shown that manifolds admitting minimal genus weakly reducible but irreducible Heegaard splittings contain an essential surface. This is an extension of a well known theorem of Casson-Gordon to manifolds with non-empty boundary. The situation for non-minimal genus Heegaard splittings is also investigated and it is shown that boundary stabilizations are stabilizations for manifolds which are boundary primitive.

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