Volume 7, issue 3 (2007)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Pullbacks of generalized universal coverings

Hanspeter Fischer

Algebraic & Geometric Topology 7 (2007) 1379–1388
Abstract

It is known that there is a wide class of path-connected topological spaces X, which are not semilocally simply-connected but have a generalized universal covering, that is, a surjective map p : X̃ X which is characterized by the usual unique lifting criterion and the fact that X̃ is path-connected, locally path-connected and simply-connected.

For a path-connected topological space Y and a map f : Y X, we form the pullback fp : fX̃ Y of such a generalized universal covering p : X̃ X and consider the following question: given a path-component of fX̃, when exactly is fp| : Y a generalized universal covering? We show that the classical criterion, of f# : π1(Y ) π1(X) being injective, is too coarse a notion to be sufficient in this context and present its appropriate (necessary and sufficient) refinement.

Keywords
generalized covering space, pullback, fibered product
Mathematical Subject Classification 2000
Primary: 55R65
Secondary: 57M10, 54B99
References
Publication
Received: 14 January 2007
Revised: 29 May 2007
Accepted: 28 August 2007
Published: 24 September 2007
Authors
Hanspeter Fischer
Department of Mathematical Sciences
Ball State University
Muncie
IN 47306
U.S.A.
http://www.cs.bsu.edu/~fischer/