Title: The fundamental groups of Haken n-manifolds
Speaker: Tharatorn Supasiti
Abstract: Historically, there have been two main approaches in the study of 3-manifolds. In particularly, the approach introduced by Haken is proven successful in computational topology, when restricted to a class of 3-manifolds called Haken manifold. Recently, Foozwell extended some properties of Haken manifolds to higher dimensions, with emphasis on dimension four. In his thesis, he was able to adapt Waldhausen's algorithm to conclude that the topological word problem is solvable for any fundamental group of Haken n-manifold. This prompts the following question: under what condition, is the fundamental group of a Haken n-manifold, word-hyperbolic? In this talk, I will address my current progress on answering this question.