Tornehave Morphisms I: Resurrecting the Virtual Permutation Sets Annihilated by Linearization

Abstract

Tom Dieck introduced a commutative triangle whereby the exponential morphism from the Burnside functor to the unit functor is factorized through the real representation functor. Tornehave introduced a p-adic variant of the exponential morphism. His construction involves real representations that are not well defined up to isomorphism. To obtain a well defined commutative triangle, we introduce the orientation functor, a quotient of the real representation functor.

Key Words:

• Burnside functor
• Orientation functor
• Unit functor
• Zombie module

2000 Mathematics Subject Classification:

• Primary 19A22
• Secondary 20C15

Notes

Communicated by J. Zhang.