USA Topology Seminar
Incoherent negatively curved groups
Josh Barnard, University of South Alabama
Friday, March 27, 2009
We discuss Dani Wise's version of a construction of Rips. Given a finitely presented group Q, this construction produces a group G, which is the fundamental group of a negatively curved 2-complex, with the property that G/N=Q for some finitely generated kernel N. By choosing suitable Q, we thus find negatively curved groups G with interesting properties, among which are (i) the existence of finitely generated subgroups with infinitely generated intersection; (ii) the existence of finitely generated subgroups that are not finitely presented; (iii) unsolvability of the generalized word-problem.