Geodesic
Locally unknotted spines of Heegaard splittings
Johnson, Jesse1
1Mathematics Department, University of California, Davis CA 95616, USA
Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1573-1584
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We show that under reasonable conditions, the spines of the handlebodies of a strongly irreducible Heegaard splitting will intersect a closed ball in a graph which is isotopic into the boundary of the ball. This is in some sense a generalization of the results by Scharlemann on how a strongly irreducible Heegaard splitting surface can intersect a ball.

DOI : 10.2140/agt.2005.5.1573
Keywords: Heegaard splitting, sweep-out, locally unkotted spine

Johnson, Jesse  1

1 Mathematics Department, University of California, Davis CA 95616, USA 
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Johnson, Jesse. Locally unknotted spines of Heegaard splittings. Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1573-1584. doi: 10.2140/agt.2005.5.1573

[1] A J Casson, C M Gordon, Reducing Heegaard splittings, Topology Appl. 27 (1987) 275

[2] J Cerf, Sur les difféomorphismes de la sphère de dimension trois $(\Gamma_{4}=0)$, Lecture Notes in Mathematics 53, Springer (1968)

[3] H Rubinstein, M Scharlemann, Comparing Heegaard splittings of non–Haken 3–manifolds, Topology 35 (1996) 1005

[4] M Scharlemann, Local detection of strongly irreducible Heegaard splittings, Topology Appl. 90 (1998) 135

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