On Weil homomorphism in locally free sheaves over structured spaces

• Autorzy: Falkiewicz E. , Sasin W.

Identyfikatory

DOI

10.1515/dema-2017-0003

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

structured space; locally free sheaf; linear connection; curvature; Weil homomorphism; invariant forms

PL

przestrzeń strukturalna; przestrzeń uporządkowana; koneksje liniowe; połączenie liniowe; krzywizna; homomorfizm Weila; formy uporządkowane

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2017
• Tom: Vol. 50, nr 1
• Strony: 28--41
• Opis fizyczny: Bibliogr. 10 poz., tab.

Twórcy

autor

Falkiewicz E.

• Department of Mathematics, Radom University of Technology, Malczewskiego 20a, 26-600 Radom, Poland

autor

Sasin W.

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warszawa, Poland

Bibliografia

• [1] Heller M., Sasin W., Structured spaces and their application to relativistic physics, J. Math. Phys., 1995, 36 (7), 3644-3662
• [2] Sikorski R., Introduction to differential geometry (in Polish), PWN, Warsaw, 1972
• [3] Sasin W., Żekanowski Z., On some sheaves over a differential space, Arch. Math. 4, Scripta Fac. Sci. Nat. UJ EP BRUNENSIS, 1982, 18, 193-199
• [4] Mallios A., Geometry of vector sheaves. An axiomatic approach to differential geometry, vol.I: Vector sheaves. General Theory, Kluwer Academic Publishers, 1998
• [5] Mallios A., Geometry of vector sheaves. An axiomatic approach to differential geometry, vol.II: Geometry. Examples and Applications, Kluwer Academic Publishers, 1998
• [6] Sasin W., On Weil homomorphism in locally free sheaves over a differential space, Demonstratio Math., 1983, 16 (3), 699-711
• [7] Falkiewicz E., An algebraic approach to Weil homomorphism on differential spaces, PhD thesis (in Polish), Warsaw, 2012
• [8] Hirzebruch F., Topological methods in algebraic geometry, Springer Verlag, Berlin, Heidelberg, New York, 1978
• [9] Nakahara M., Geometry, topology and physics, second edition, Institute of Physics Publishing, Bristol and Philadelphia, 2003
• [10] Milnor J. W., Stasheff J. D., Characteristic classes, Princeton University Press and University of Tokyo Press, Princeton, New Yersey, 1974

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).