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Covering maps that are not compositions of covering maps of lesser order

Author(s): Jerzy Krzempek
Journal: Proc. Amer. Math. Soc. 130 (2002), 1867-1873.
MSC (2000): Primary 54C10; Secondary 05C25
Posted: November 15, 2001
MathSciNet review: 1887036
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Abstract: In 1995 J.W. Heath asked which exactly -to-one maps are compositions of exactly -to-one maps with . This paper deals with compositions of covering maps. Exactly -to-one covering maps on locally arcwise connected continua that are not factorable into covering maps of order $\leq n-1$ are constructed for all 's, and characterized in algebraic terms (fundamental groups). They are not proper compositions of exactly -to-one maps, open maps, or locally one-to-one maps.

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Additional Information:

Jerzy Krzempek
Affiliation: Institute of Mathematics, Silesian Technical University, Kaszubska 23, PL-44-100 Gliwice, Poland
Email: krzem@zeus.polsl.gliwice.pl

DOI: 10.1090/S0002-9939-01-06266-9
PII: S 0002-9939(01)06266-9
Keywords: Composition, covering map, locally one-to-one, open, exactly $k$-to-one map, group action, fundamental group
Received by editor(s): November 6, 2000
Received by editor(s) in revised form: January 9, 2001
Posted: November 15, 2001
Communicated by: Alan Dow
Copyright of article: Copyright 2001, American Mathematical Society

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