Geodesic
Sweepouts of amalgamated 3–manifolds
Bachman, David1 ; Schleimer, Saul2 ; Sedgwick, Eric3
1Mathematics Department, Pitzer College, 1050 North Mills Avenue, Claremont CA 91711, USA
2Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd, Piscataway NJ 08854-8019, USA
3CTI, DePaul University, 243 S Wabash Avenue, Chicago IL 60604, USA
Algebraic and Geometric Topology, Tome 6 (2006) no. 1, pp. 171-194
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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.

DOI : 10.2140/agt.2006.6.171
Keywords: Heegaard splitting, incompressible surface

Bachman, David  1   ; Schleimer, Saul  2   ; Sedgwick, Eric  3

1 Mathematics Department, Pitzer College, 1050 North Mills Avenue, Claremont CA 91711, USA
2 Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd, Piscataway NJ 08854-8019, USA
3 CTI, DePaul University, 243 S Wabash Avenue, Chicago IL 60604, USA 
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Bachman, David; Schleimer, Saul; Sedgwick, Eric. Sweepouts of amalgamated 3–manifolds. Algebraic and Geometric Topology, Tome 6 (2006) no. 1, pp. 171-194. doi: 10.2140/agt.2006.6.171

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