Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Frobenius n-homomorphisms, transfers and branched coverings

V. M. BUCHSTABERa1, V. M. BUCHSTABERa2 and E. G. REESa2

a1 Steklov Mathematical Institute, RAS, Gubkina 8, 119991 Moscow and School of Mathematics, University of Manchester, Manchester M13 9PL.

a2 School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ and Heilbronn Institute for Mathematical Research, University of Bristol, Bristol BS8 1TW.

Abstract

The main purpose is to characterise continuous maps that are n-branched coverings in terms of induced maps on the rings of functions. The special properties of Frobenius n-homomorphisms between two function spaces that correspond to n-branched coverings are determined completely. Several equivalent definitions of a Frobenius n-homomorphism are compared and some of their properties are proved. An axiomatic treatment of n-transfers is given in general and properties of n-branched coverings are studied and compared with those of regular coverings.

(Received August 20 2006)

(Revised December 12 2006)