%0 Journal Article
%T A topologically minimal, weakly reducible, unstabilized Heegaard splitting of genus three is critical
%A Jungsoo Kim
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1402.4253v4