Algebraic & Geometric Topology 6 (2006) 171–194

DOI: 10.2140/agt.2006.6.171

arXiv: math.GT/0507490

Abstract

We show that if two 3–manifolds with toroidal boundary are glued via a “sufficiently complicated” map then every Heegaard splitting of the resulting 3–manifold is weakly reducible. Additionally, suppose X ∪_FY is a manifold obtained by gluing X and Y , two connected small manifolds with incompressible boundary, along a closed surface F. Then the following inequality on genera is obtained:

Both results follow from a new technique to simplify the intersection between an incompressible surface and a strongly irreducible Heegaard splitting.

Keywords

Heegaard splitting, incompressible surface

Mathematical Subject Classification

Primary: 57M99, 57N10

Secondary: 57M27

References

Publication

Received: 26 July 2005
Revised: 18 January 2006
Accepted: 26 January 2006
Published: 24 February 2006

Authors