A classification of cohomology transfers for ramified covering maps

Marcelo A. Aguilar ¹   ; Carlos Prieto ²

¹ Instituto de Matemáticas UNAM 04510 México, D.F., Mexico
² Instituto de Matemáticas UNAM 04510 México, D.F. Mexico

Fundamenta Mathematicae, Tome 189 (2006) no. 1, pp. 1-25

Résumé

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.

Détail

DOI : 10.4064/fm189-1-1

Keywords: construct cohomology transfer n fold ramified covering maps define general concept transfer ramified covering maps prove classification theorem transfers generalizes roushs classification transfers n fold ordinary covering maps characterize those representable cofunctors which admit family transfers ramified covering maps have naturality properties normalization stability analogous roushs characterization theorem ordinary covering maps finally classify those families transfers construct examples particular extend determinant function mathbb transfer