[Binghamton Geometry/Topology Seminar] March 25

[Marco Varisco]

Dean's Speaker Series in Geometry/Topology
http://www.math.binghamton.edu/dept/topsem/

Date: Thursday, March 25, 2010

Time: 2:50–3:50 pm

Place: Library North 2205
(followed by coffee/tea in the Anderson Reading Room)

Speaker: Søren Galatius (Stanford University)

Title: Monoids of moduli spaces of manifolds

Abstract: I will discuss joint work with Oscar Randal-Williams, where
we study the moduli spaces of Riemann surfaces equipped with
continuous maps to some space X. If Mg,1(X) denotes the space of genus
g Riemann surfaces with one parametrized boundary component, equipped
with a continuous map to X which takes the boundary to the base point
of X, we can form the limit M∞(X) by gluing tori onto the boundary
component. Madsen and Weiss' theorem determines the homology of the
space M∞(point). Cohen and Madsen extended this result to all simply
connected spaces X. My talk will describe how to remove the simple
connectedness hypothesis. At the same time we give a new proof of
Madsen-Weiss' theorem; our proof does not depend on homological
stability.