Abstract
The notion of a graded bundle is introduced. Although every smooth graded bundle is trivial nevertheless holomorphic graded bundles may not be trivial, i.e. graded elements in their transition functions not always may be all reduced to numbers as it was proved in [7]. The geometry of graded bundles and spaces of graded bundles are explored. It is shown that the differential geometrical construction of Chern classes may be possible only in special cases of graded bundles. The families of graded bundles over instanton solutions of field theory are discussed. A few open problems are mentioned.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
AKULOV, V.P., D.V. VOLKOV, Phys. Lett., B 46 (1973), 109–110.
ANOWITT, R., P. NATH, B. ZUMINO, Phys. Lett., B56(1975), 81–84.
ATIYAH, M.F., R.S. WARD, Comm. Math. Phys. 55(1977), 117–124.
BATHEROL, M., Trans. Amer. Math. Soc., to appear.
BEREZIN, F.A., A.A. LEYTES, Dokl. Akad. Nauk SSSR, 224(1975), 505–508.
CHERN, S.S., "Complex manifolds without potential theory", Princeton, 1967, D.Van Nostrand.
CZYZ, J., submitted to Comm. Math. Phys.
DELL, J., L. SMOLIN, Comm. Math. Phys. 66(1979), 197–222.
DESER, S., "Differential Geometrical Mathods in Mathematical Physics II" Lecture Notes in Math., 676, Berlin 1978, Springer, 573–596.
—, "Group theoretical Methods in Physics", Lecture Notes in Phys., 94, Berlin, 1979, Springer, 468–476.
DRINFELD, V.G., Ju.I. MANIN, Comm. Math. Phys., 63(1978), 177–192.
—, Jaderna’a fizika, 29(1979), 1646–1655, (in Russian).
FEYNMAN, R.P., R.B. LEIGHTON, M. SANDS, "The Feynman Lectures on Physics III", Reading, 1965, Addison-Wesley.
GAWEDZKI, K., Ann. Inst. Henri Poincareé, 27(1977), 335–366.
GODEMAN, R., "Topologie algébraique et theorie des fais-ceaux", Paris, 1958, Alermann.
HAAG, R., J.T. ŁOPUSZANSKI, M. SOHNIUS, Nucl. Phys. B88(1975), 257–274.
HARTSHORNE, R., Comm. Math. Phys., 59(1978), 1–16.
HIRZEBRUCH, F., "Topological Matheods in Algebraic Geometry", Berlin, 1968, Springer.
KAC, V.G., Comm. Math. Phys., 53(1977), 31–64.
KOSTANT, B., "Differential Geometrical Mathods in Mathematical Physics", Lecture Notes in Math., 570, Berlin, 1977, Springer.
KOTECKY, R., Rept. Math. Phys., 7 (1975), 457–469.
MAURIN, K., "Analysis, Part II", to appear in PWN — D.Reidel.
NEEMAN, Y., "Differential Geometrical Methods in Mathematical Physics", Lecture Notes in Math., 570, Berlin, 1977, Springer, 109–144.
NIEDERLE, J., preprint IC/79/136.
ROGERS, A., preprint ICTP/78-79/15.
SCHWARZ, A.S., Comm. Math. Phys., 64(1979), 233–268.
STEENROD, N., "The Topology of Fibre Bundles", Princeton, 1951.
STERNBERG, S., "Differential Geometrical Methods in Mathematical Physics", Lecture Notes in Math., 570, Berlin, 1977, Springer, 145–176.
WELLS, R.O. jr., Bull. Amer. Math. Soc. 1(1979), 296–337.
WESS, J., B. ZUMINO, Nucl. Phys., B70(1974), 39–50.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag
About this paper
Cite this paper
Czyż, J. (1981). On graded bundles and their geometry. In: Ferus, D., Kühnel, W., Simon, U., Wegner, B. (eds) Global Differential Geometry and Global Analysis. Lecture Notes in Mathematics, vol 838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088847
Download citation
DOI: https://doi.org/10.1007/BFb0088847
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10285-4
Online ISBN: 978-3-540-38419-9
eBook Packages: Springer Book Archive