engleski

Finite-Sheeted Covering Maps over Compact Connected Groups

Recently, the classification theorem of finite-sheeted covering maps over paracompact spaces has been proved. It establishes a bijection between the set of all pointed equivalence classes of s-sheeted pointed covering maps f:(X, *)→ (Y, *) over connected paracompact space (Y, *) and the set of all subprogroups of index s of the fundamental progroup of (Y, *). Using this result we classify finite-sheeted covering maps over 2-dimensional connected, compact abelian group, i.e. inverse limit of 2-dimensional tori. Furthermore, in some special cases we examine whether a total space is homeomorphic to the base space . The proof of our classification theorem is reduced only to the case of finite-sheeted covering homomorphisms since each finite-sheeted covering map f:X→ Y over a connected, compact group Y admits a (unique) multiplication on X such that X is a topological group and f homomorphism.

Compact group; compact abelian group; finite-sheeted covering; covering homomorphism.

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