- Tytuł:
- Fundamental pro-groupoids and covering projections
- Autorzy:
- Hernández-Paricio, Luis
- Powiązania:
- https://bibliotekanauki.pl/articles/1205368.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
covering projection
covering transformation
pro-groupoid, Čech fundamental pro-groupoid
covering reduced sieve
locally constant presheaf
category of fractions
subdivision
fundamental groupoid
Čech fundamental group
G-sets
continuous G-sets - Opis:
- We introduce a new notion of covering projection E → X of a topological space X which reduces to the usual notion if X is locally connected. We use locally constant presheaves and covering reduced sieves to find a pro-groupoid π crs (X) and an induced category pro (π crs (X), Sets) such that for any topological space X the category of covering projections and transformations of X is equivalent to the category pro (π crs (X), Sets). We also prove that the latter category is equivalent to pro (π CX, Sets), where π CX is the Čech fundamental pro-groupoid of X. If X is locally path-connected and semilocally 1-connected, we show that π crs (X) is weakly equivalent to π X, the standard fundamental groupoid of X, and in this case pro (π crs (X), Sets) is equivalent to the functor category $Sets^{π X}$. If (X,*) is a pointed connected compact metrisable space and if (X,*) is 1-movable, then the category of covering projections of X is equivalent to the category of continuous $\check π_1 (X,*)$-sets, where $\check π_1 (X,*)$ is the Čech fundamental group provided with the inverse limit topology.
- Źródło:
-
Fundamenta Mathematicae; 1998, 156, 1; 1-31
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł