August 2017 September 2017 |

4:00 pm Monday, September 18, 2017 Topology Seminar: The period mapping on outer spaceby Neil Fullarton (Rice) in HBH 227- (This is joint work with Corey Bregman.) Given a basis of 1-cycles in a finite graph, we can construct an inner product on the graph's homology. Using this, we define the 'period mapping' from the moduli space of marked, metric graphs (Culler--Vogtmann's 'outer space') to the moduli space of marked, flat tori, two very well-studied spaces. I'll discuss basic properties of this map, and compare with the more classical period mapping for Riemann surfaces. Our main result explicitly determines the homotopy type of the fibers of this graph-theoretic period mapping. I'll also discuss how the space of marked, so-called 'hyperelliptic' graphs behaves as a branch locus for the mapping, and how we show that this locus is, in a sense, simply-connected at infinity.
Submitted by neil.fullarton@rice.edu |