A topologically minimal, weakly reducible, unstabilized Heegaard splitting of genus three is critical
Abstract
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 two if F is topologically minimal.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2014
- DOI:
- 10.48550/arXiv.1402.4253
- arXiv:
- arXiv:1402.4253
- Bibcode:
- 2014arXiv1402.4253K
- Keywords:
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- Mathematics - Geometric Topology;
- 57M50
- E-Print:
- 20 pages, 11 figures. More detailed arguments and figures