Abstract
Fiber bundles, their morphisms and sections are defined. Transition functions are introduced and used to describe the global structure of a bundle and to build it out of local data. Particular classes of fiber bundles (affine bundles, vector bundles and principal bundles) are introduced. Bundles are then provided with the further structure of fiber bundles with structure group,which will be used below as prototypes of configuration bundles in Field Theory. The Hopf bundle, the tangent bundle and the frame bundle are considered all along in detail as examples.
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
C. Rovelli, M. Francaviglia, Elements of Differential and Riemannian Geometry, Bibliopolis, Napoli, 1988 Italy
C. Rovelli, M. Göckeler, T. Schücker, Differential Geometry, Gauge Theories and Gravity, Cambridge University Press, New York, 1987 USA
C. Rovelli, R.O. Wells, Differential Analysis on Complex Manifolds, Graduate Texts in Mathematics, Springer — Verlag, New York 1980
C. Rovelli, Y. Choquet-Bruhat, Géométrie Différentielle et Systémes Extérieurs, Dunod Paris, 1968
C. Rovelli, Y. Choquet-Bruhat, C. DeWitt-Morette, Analysis, Manifolds and Physics, North-Holland, Amsterdam, 1982
C. Rovelli, S. Mac Lane, Categories for Working Mathematician, Springer — Ver-lag, New York 1971
H. Herrlich, G.E. Strecker, Category theory: an introduction, Helder-mann, Berlin, 1979
C. Rovelli, B.R. Tennison, Sheaf Theory, London Mathematical Society Lectu re Notes Series, 20 Cambridge University Press, Cambridge 1975
C. Rovelli, V. Guillemin, A. Pollack Differential Topology, Prentice — Hall, Inc., Eaglewood Cliffs, New Jersey, 1974
C. Rovelli, E.H. Spanier, Algebraic Topology, McGraw — Hill, Berkeley, 1966 USA
C. Rovelli, M. Palese, Ph.D. Thesis, University of Torino, Italy, 1999
C. Rovelli, J. Milnor, J.D. Stasheff, Characteristic Classes, Ann. of Math. Studies 76, Princeton University Press, Princeton 1963
C. Rovelli, S. Kobayashi, K. Nomizu, Foundations of differential geometry, John Wiley & Sons, Inc., New York, 1963 USA
C. Rovelli, N. Steenrod, Topology of Fibre Bundles, Princeton University Press, Princeton, 1951 USA
C. Rovelli, J. Baez, J.P. Munian, Gauge Fields, Knots and Gravity, World Scientific, Singapore, 1994
C. Rovelli, D. Bleecker, Gauge theory and variational principles, Addison-Wesley Publishing Company, Inc., Massachussetts, 1981
C. Rovelli, M. Nakahara, Geometry, Topology and Physics, Institute of Publishing, Bristol, 1990 UK
C. Rovelli, K.B. Marathe, G. Martucci, The mathematical foundations of gauge theories, North — Holland, Amsterdam, 1992 Holland
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Fatibene, L., Francaviglia, M. (2003). Fiber Bundles. In: Natural and Gauge Natural Formalism for Classical Field Theorie. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2384-8_1
Download citation
DOI: https://doi.org/10.1007/978-94-017-2384-8_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6461-5
Online ISBN: 978-94-017-2384-8
eBook Packages: Springer Book Archive