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

Krzempek, Jerzy

doi:10.1090/S0002-9939-01-06266-9

Covering maps that are not compositions of covering maps of lesser order
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Proc. Amer. Math. Soc. 130 (2002), 1867-1873 Request permission

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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