New versions of the fundamental group and covering space theory
by
Peter Johnson
Univ. Federal de Pernambuco

For connected and locally path-connected (pointed) topological spaces, there is a well-developed theory relating covering spaces to subgroups of the fundamental group. The latter group acts as the group of deck transformations of a universal covering space, whose existence is assured if certain conditions are met. Paths seem to play an essential role in this well-known theory that relates covers and subgroups.

We shall instead develop, using ideas that mix incidence geometry and topology, an alternate and completely path-free approach to the classification of covers of general topological spaces (without going beyond that category, as others such as Grothendieck do). It gives particularly good results for locally connected spaces. In place of the fundamental group, which can fail to give the desired results unless the space is at least locally connected, we define another group which works in general.

Date received: February 19, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagg-05.