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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Jerzy Krzempek
Journal: Proc. Amer. Math. Soc. 130 (2002), 1867-1873
MSC (2000): Primary 54C10; Secondary 05C25
Published electronically: November 15, 2001
MathSciNet review: 1887036
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Abstract: In 1995 J.W. Heath asked which exactly $n$-to-one maps are compositions of exactly $k$-to-one maps with $1<k<n$. This paper deals with compositions of covering maps. Exactly $n$-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 $n$'s, and characterized in algebraic terms (fundamental groups). They are not proper compositions of exactly $k$-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: http://dx.doi.org/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
Published electronically: November 15, 2001
Communicated by: Alan Dow
Article copyright: © Copyright 2001 American Mathematical Society