Sweepouts of amalgamated 3-manifolds
By David Bachman, Saul Schleimer, E. Sedgwick. 2005
47 citations recorded by the source corpus.
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[F Y 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: g.X[F Y/ 1 .g.X/Cg.Y/ 2g.F//: Both results follow from a new technique to simplify the intersection between an incompressible surface and a strongly irreducible Heegaard splitting. 57N10, 57M99; 57M27
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d1ff254f59a014b2ac5c26d2da0fd37946bb82c1
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Heegaard surfaces and the distance of amalgamation (2008, background): “2 (Bachman–Schleimer–Sedgwick [2]) Let Ni be a compact, irreducible, orientable 3–manifold with @Ni incompressible, if nonempty.”
- Topological Index Theory for surfaces in 3-manifolds (2009, methodology): “Versions of this result were obtained by Schultens for graph manifolds [22], and the author, Sedgwick and Schleimer for more general Haken manifolds [7].”