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2007 Pullbacks of generalized universal coverings
Hanspeter Fischer
Algebr. Geom. Topol. 7(3): 1379-1388 (2007). DOI: 10.2140/agt.2007.7.1379


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:X̃X 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:YX, we form the pullback fp:fX̃Y of such a generalized universal covering p:X̃X 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.


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Hanspeter Fischer. "Pullbacks of generalized universal coverings." Algebr. Geom. Topol. 7 (3) 1379 - 1388, 2007.


Received: 14 January 2007; Revised: 29 May 2007; Accepted: 28 August 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1131.55009
MathSciNet: MR2350286
Digital Object Identifier: 10.2140/agt.2007.7.1379

Primary: 55R65
Secondary: 54B99, 57M10

Rights: Copyright © 2007 Mathematical Sciences Publishers


Vol.7 • No. 3 • 2007
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