Geodesic
A topologically minimal, weakly reducible, unstabilized Heegaard splitting of genus three is critical
Kim, Jungsoo1
1BK21 PLUS SNU Mathematical Sciences Division, Seoul National University, 1 Gwanak-ro, Gwanak-Gu, Seoul 08826, South Korea
Algebraic and Geometric Topology, Tome 16 (2016) no. 3, pp. 1427-1451
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Let (V,W;F) be a weakly reducible unstabilized genus three Heegaard splitting in an orientable, irreducible 3–manifold M. In this article, we prove that either the disk complex D(F) is contractible or F is critical. Hence, the topological index of F is 2 if F is topologically minimal.

DOI : 10.2140/agt.2016.16.1427
Classification : 57M50
Keywords: $3$–manifold, Heegaard splitting, disk complex, topologically minimal surface

Kim, Jungsoo  1

1 BK21 PLUS SNU Mathematical Sciences Division, Seoul National University, 1 Gwanak-ro, Gwanak-Gu, Seoul 08826, South Korea 
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Kim, Jungsoo. A topologically minimal, weakly reducible, unstabilized Heegaard splitting of genus three is critical. Algebraic and Geometric Topology, Tome 16 (2016) no. 3, pp. 1427-1451. doi: 10.2140/agt.2016.16.1427

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