A classification of cohomology transfers for ramified coverings

Primary 55R12, 57M12; Secondary 55Q05, 55R35, 57M10

Transfer, covering maps, ramified covering maps, classifying spaces  

Marcelo A. Aguilar and  Carlos Prieto

cprieto@math.unam.mx, marcelo@math.unam.mx


Abstract

We construct a cohomolgy transfer for $n$-fold ramified covering maps. Then, we define a very general concept of transfer for ramified covering maps and prove a classification theorem for these transfers. This generalizes Roush's classification of transfers for $n$-fold ordinary covering maps. We characterize those representable cofunctors which admit a family of transfers for ramified covering maps that have two naturality properties, as well as normalization and stability.  This is analogous to Roush's characterization theorem for the case of ordinary covering maps. Finally, we classify these families of transfers and construct some examples. In particular, we extend the determinant function in $\GL(k,\C)$ to a transfer.