We start with the universal covering space $\tilde M^n$ of a closed n-manifold and with a tree of fundamental domains which zips it $T\longarrow \tilde M^n$. Our result is that, between $T$ and $\tilde M^n$, is an intermediary object , $T\rto^p G \rTo^F \tilde M^n$, obtained by zipping, such that each fiber of p is FINITE and $T\rto^p G \rTo^F \tilde M^n$ admits a SECTION.
POENARU, V., TANASI, C. (2008). A Group-theoretical Finiteness Theorem. GEOMETRIAE DEDICATA, 137, 1-25 [10.1007/s10711-008-9279-4].
A Group-theoretical Finiteness Theorem
TANASI, Corrado
2008-01-01
Abstract
We start with the universal covering space $\tilde M^n$ of a closed n-manifold and with a tree of fundamental domains which zips it $T\longarrow \tilde M^n$. Our result is that, between $T$ and $\tilde M^n$, is an intermediary object , $T\rto^p G \rTo^F \tilde M^n$, obtained by zipping, such that each fiber of p is FINITE and $T\rto^p G \rTo^F \tilde M^n$ admits a SECTION.
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