TY - JOUR

T1 - Finite sheeted covering maps over 2-dimensional connected, compact Abelian groups

AU - Eda, Katsuya

AU - Matijević, Vlasta

PY - 2006/1/1

Y1 - 2006/1/1

N2 - Let G be a 2-dimensional connected, compact Abelian group and s be a positive integer. We prove that a classification of s-sheeted covering maps over G is reduced to a classification of s-index torsionfree supergroups of the Pontrjagin dual Ĝ. Using group theoretic results from earlier paper we demonstrate its consequences. We also prove that for a connected compact group Y: (1) Every finite-sheeted co vering map from a connected space over Y is equivalent to a covering homomorphism from a compact, connected group. (2) If two finite-sheeted covering homomorphisms over Y are equivalent, then they are equivalent as topological homomorphisms.

AB - Let G be a 2-dimensional connected, compact Abelian group and s be a positive integer. We prove that a classification of s-sheeted covering maps over G is reduced to a classification of s-index torsionfree supergroups of the Pontrjagin dual Ĝ. Using group theoretic results from earlier paper we demonstrate its consequences. We also prove that for a connected compact group Y: (1) Every finite-sheeted co vering map from a connected space over Y is equivalent to a covering homomorphism from a compact, connected group. (2) If two finite-sheeted covering homomorphisms over Y are equivalent, then they are equivalent as topological homomorphisms.

KW - 2-dimensional

KW - Compact Abelian group

KW - Compact group

KW - Finite-sheeted covering

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U2 - 10.1016/j.topol.2005.02.005

DO - 10.1016/j.topol.2005.02.005

M3 - Article

AN - SCOPUS:31844433993

SN - 0166-8641

VL - 153

SP - 1033

EP - 1045

JO - Topology and its Applications

JF - Topology and its Applications

IS - 7

ER -