Title: Flats and Essential Tori in Cubed Manifolds
Speaker: Tharatorn Supasiti (University of Melbourne)
Abstract: The Weak Hyperbolisation Theorem states that the fundamental group of a closed 3-manifold is either word-hyperbolic, or else, it contains a free abelian subgroup of rank 2. In the context of a group G acting cocompactly and properly discontinuously on a CAT(0) space X, it is unknown that whether or not the ℤ2 subgroup is the only obstruction to word-hyperbolicity of G. However, under the same hypothesis, it has been shown that if G is not word-hyperbolic, then there is an isometric embedding of Euclidean plane into X. And this suggests that G may contain ℤ2 as a subgroup. There are many interesting cases where this is true. In this talk, I will discuss this question when G is the fundamental group of a cubed n-manifold.