Heegaard genus formula for Haken manifolds

Details Heegaard genus formula for Haken manifolds Heegaard genus formula for Haken manifolds

2001-08-03

arxiv.org/abs/math/0108028v3

Mathematics

Geometric Topology

21 pages, 17 figures

Scientific paper

Given a 3-manifold M containing an incompressible surface Q, we obtain an inequality relating the Heegaard genus of M and the Heegaard genera of the components of M - Q. Here the sum of the genera of the components of M - Q is bounded above by a linear expression in terms of the genus of M, the Euler characteristic of Q and the number of parallelism classes of essential annuli for which representatives can be simultaneously imbedded in the components of M - Q.

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