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 3manifold 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:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.4253
 Bibcode:
 2014arXiv1402.4253K
 Keywords:

 Mathematics  Geometric Topology;
 57M50
 EPrint:
 20 pages, 11 figures. More detailed arguments and figures