Classifying Finite-Sheeted Covering Mappings of Paracompact Spaces
by
Vlasta Matijevic
Department of mathematics University of Split

The well-known classical classification theorem of the covering space theory refers to covering mappings of connected spaces, where the base space is locally pathwise connected and semi-locally 1-connected. Here, we give a classification theorem for finite-sheeted covering mappings over connected paracompact spaces. It establishes a bijection between the set of all pointed equivalence classes of s-sheeted pointed covering mappings f:(X, * ) --> (Y, * ) over connected paracompact space (Y, * ) and the set of all subprogroups of index s of the fundamental progroup \pi₁(Y, * ). In the unpointed case it establishes a bijection between the set of all of all equivalence classes of s-sheeted covering mappings f: X --> Y and the set of all conjugacy classes of subprogroups of index s of the fundamental progroup \pi₁(Y, * ), where * is an arbitrary chosen point of Y. Finite-sheeted covering mappings of torus-like continua will be considered, as an application of the theorem.

References:
[1] V. Matijevi\'c, Classifying finite-sheeted covering mappings of paracompact spaces, (to appear in Revista Matematica Complutense).

Date received: August 31, 2002

Copyright © 2002 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 # caje-74.