Chennai Mathematical Institute


3:30 pm, Seminar Hall
Inverse monoids and immersions of CW-complexes

John Meakin
Univresity of Nebraska-Lincoln, USA.


It is well known that under mild conditions on a connected topological space $\chi$, connected covers of $\chi$ may be classified via conjugacy classes of subgroups of the fundamental group of $\chi$. In this talk, we extend these results to the study of immersions into 2-dimensional CW-complexes. An immersion $f : {\cal D} \rightarrow {\cal C}$ between CW-complexes is a cellular map such that each point $y \in {\cal D}$ has a neighborhood $U$ that is mapped homeomorphically onto $f(U)$ by $f$. In order to classify immersions into a 2-dimensional CW-complex ${\cal C}$, we need to replace the fundamental group of ${\cal C}$ 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 Nara Szakacs.