On Weil homomorphism in locally free sheaves over structured spaces

Abstract

Inspired by the work of Heller and Sasin [1], we construct in this paper Weil homomorphism in a locally free sheaf W of ϕ-fields [2] over a structured space. We introduce the notion of G-consistent, linear connection on this sheaf, what allows us to clearly define Chern, Pontrjagin and Euler characteristic classes. We also show proper equalities between those classes.

Keywords

• Structured space
• Locally free sheaf
• Linear connection
• Curvature
• Weil homomorphism
• Invariant forms
• 14F05
• 53B05
• 57R20