6533b830fe1ef96bd129684c

RESEARCH PRODUCT

A Group-theoretical Finiteness Theorem

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We start with the universal covering space $${\*M^n}$$ of a closed n-manifold and with a tree of fundamental domains which zips it $${T\longrightarrow\*M^n}$$ . Our result is that, between T and $${\* M^n}$$ , is an intermediary object, $${T\stackrel{p} {\longrightarrow} G \stackrel{F}{\longrightarrow} \*M^n}$$ , obtained by zipping, such that each fiber of p is finite and $${T\stackrel{p}{\longrightarrow}G\stackrel{F}{\longrightarrow} \*M^n}$$ admits a section.