Date & Time: Wednesday, January 15, 2014, 14:30-15:30.
Venue: Ramanujan Hall
Speaker: John Meakin, University of Nebraska-Lincoln
Title: Inverse Monoids and Immersions of CW-complexes
Abstract: It is well known that under mild conditions on a connected topological space X, connected covers of X may be classified via conjugacy classes of subgroups of the fundamental group of X. In this talk, we extend these results to the study of immersions into 2-dimensional CW-complexes.
An immersion f from D to C between CW-complexes is a cellular map such that each point y in D has a neighborhood U that is mapped homeomorphically onto f(U) by f. In order to classify immersions into a 2-dimensional CW-complex C, we need to replace the fundamental group of C by an appropriate inverse monoid.
In this talk I will survey the necessary inverse monoid theory and describe the connections between closed inverse submonoids of inverse monoids and immersions between CW-complexes. Part of this work is joint with Stuart Margolis and part is joint with Nora Szakacs.
I will gear the talk towards a general mathematical audience.