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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.

Riemannian vector bundles have no canonical linear conections

Mikulski W.

Demonstratio Mathematica

2009

Vol. 42, nr 1

233-236

We prove that Riemannian vector bundles have no canonical linear connections.

Reduction for natural operators on projectable connections

Mikulski M., Tomas J.

Demonstratio Mathematica

2009

Vol. 42, nr 2

435-439

We present a very simple proof of a general reduction for natural operators on torsion free projectable classical linear connections.

Natural liftings of connections to the r-th order bundle

Mikulski W.

Demonstratio Mathematica

2007

Vol. 40, nr 2

481-484

We describe all natural operators A lifting a clasiccal linear connection on an m-dimensional manifold M into a classical linear conection A() on the r-th order frame bundle LrM = invJr/0 (Rm,M).

Negative answers to some questions about constructions on connections

Mikulski W.

Demonstratio Mathematica

2006

Vol. 39, nr 3

685-689

Let m and n be natural numbers. For an arbitrary bundle functor G on the category FMm,n of fibred manifolds with m-dimensional bases and n-dimensional fibers and their local fibered diffeomorphisms we prove that there is no FMm,n-natural operator V transforming general connections.