A classification of cohomology transfers for ramified covering maps
Volume 189 / 2006
Fundamenta Mathematicae 189 (2006), 1-25
MSC: Primary 55R12, 57M12; Secondary 55Q05, 57M10.
DOI: 10.4064/fm189-1-1
Abstract
We construct a cohomology 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 such 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 those families of transfers and construct some examples. In particular, we extend the determinant function in ${\rm G}L(k,{\mathbb C})$ to a transfer.
