[Binghamton Geometry/Topology Seminar] Geometry & Topology Seminar

[somnath at math.binghamton.edu]

Although there is no seminar this week, some of you may be very interested
in the COMBINATORICS seminar today. It is cross-listed as a topology
seminar and will happen if the weather permits.

Tuesday, October 30

Speaker: Ed Swartz (Cornell)
Title: Manifold Complexity and Face Enumeration
Time: 1:15 - 2:15
Room: LN-2205
There are several notions of complexity for three-manifolds. One such
definition was introduced by Matveev in the 90's. For a three-manifold M,
with or without boundary, his complexity of M is a nonnegative integer
c(M). Two properties of c(M) are: (A) For any n there are only finitely
many closed, irreducible orientable three-manifolds with c(M) less than n.
(B) c(M) is additive with respect to connected sums: c(M#N)=c(M)+c(N).
While there are many combinatorial measures of complexity which satisfy
(A), the natural ones to try, such as the minimum number of vertices or
tetrahedra in a simplicial triangulation of M, badly fail (B).

My goal is to see how c(M) can help understand face enumeration of
simplicial triangulations of M. I will also explore the possibility that
there might be simple combinatorial invariants which satisfy (A) and (B)
for 3-manifolds, and which have natural extensions to PL-triangulations in
higher dimensions which still satisfy (A).

The talk will assume no specialized knowledge of 3-manifolds.