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

Abstract

In 1995 J.W. Heath asked which exactly n n -to-one maps are compositions of exactly k k -to-one maps with 1 > k > n 1>k>n . This paper deals with compositions of covering maps. Exactly n n -to-one covering maps on locally arcwise connected continua that are not factorable into covering maps of order ≤ n − 1 \leq n-1 are constructed for all n n ’s, and characterized in algebraic terms (fundamental groups). They are not proper compositions of exactly k k -to-one maps, open maps, or locally one-to-one maps.