Geodesic
Pullbacks of generalized universal coverings
Fischer, Hanspeter1
1Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, U.S.A.
Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1379-1388
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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 f∗p : f∗X̃ → Y of such a generalized universal covering p : X̃ → X and consider the following question: given a path-component Ỹ of f∗X̃, when exactly is f∗p|Ỹ : Ỹ → 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.

DOI : 10.2140/agt.2007.7.1379
Keywords: generalized covering space, pullback, fibered product

Fischer, Hanspeter  1

1 Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, U.S.A. 
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Fischer, Hanspeter. Pullbacks of generalized universal coverings. Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1379-1388. doi: 10.2140/agt.2007.7.1379

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[2] H Fischer, Arc-smooth generalized universal covering spaces (2006)

[3] H Fischer, A Zastrow, Generalized universal covering spaces and the shape group (2005)

[4] E H Spanier, Algebraic topology, Springer–Verlag (1995)

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