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On Weil homomorphism in locally free sheaves over structured spaces

Falkiewicz E., Sasin W.

Demonstratio Mathematica

2017

Vol. 50, nr 1

28--41

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.

Weil homomorphism in non-commutative differential spaces

Jagodziński T., Sasin W.

Demonstratio Mathematica

2005

Vol. 38, nr 2

507--516

In this paper we construct Weil homomorphism in locally free module over a non-commutative differential space, which is a generalization of Sikorski differential space [6]. We consider real case, but the complex case can be done analogusly.