Event Type:

Topology Seminar

Date/Time:

Monday, February 14, 2011 - 04:00

Location:

Kidder 356

Local Speaker:

Abstract:

The Fibonacci group F(n) has n generators x_1,...x_n and n defining relations of the form x_i*x_{i+1} = x_{i+2}. In 1965, J. C. Conway asked for a proof that F(5) is cyclic of order 11, and this was quickly done. After that, the question of which F(n) are finite was considered and finally settled in 1990, with the last case being the group F(9), whose status was settled by M. F. XXXXXX. (Bets will be taken as to whether this group is finite or inifinte. so I will not reveal the author here.) Along the way, the problem led to considerations in three-manifold topology and computational/geometric group theory. I will survey these developments and present a recently-discovered technique that promises to aid in "batch-processing" of questions related to algebraic and geometric structures of cyclically presented groups.