SubjectsSubjects(version: 850)
Course, academic year 2019/2020
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Fibre Spaces and Gauge Fields - NMAG454
Title in English: Fibrované prostory a kalibrační pole
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 2019
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:3/1 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. Ing. Branislav Jurčo, CSc., DSc.
Class: M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Geometry
Annotation -
Last update: prof. RNDr. Vladimír Souček, DrSc. (13.09.2013)
The course is a continuation of the course 'Introduction to analysis on manifolds'. It is a basic course needed for a further study of differential geometry and global analysis, as well as for applications in mathematical physics (Yang-Mills fields).
Literature -
Last update: prof. RNDr. Vladimír Souček, DrSc. (13.09.2013)

J. Lee: Introduction to smooth manifolds, Springer, GTM 218, 2013

R. W. Sharpe: Differential geometry. Cartan's generalization of Klein's Erlangen program, Springer, GTM 166, 1997

I. Kolář, J. Slovák, P. Michor: Natural operation in differential geometry, Spinger, 2010

Syllabus -
Last update: prof. RNDr. Vladimír Souček, DrSc. (13.09.2013)

Smooth manifolds, differential forms. Distributions, Frobenius theorem (2 versions).

Fibre bundles, transition functions, vector fibre bundles, their local description, classifying maps.

Covariant derivatives on vector bundles, parallel transport, curvature, structure equations.

Homogeneous spaces, the Maurer-Cartan form, the Darboux derivative, fundamental theorem of calculus.

Principal fibre bundles, associated fiber bundles, principal connections and their curvature, structure equations.

Holonomy and monodromy. Calibration (Yang-Mills) fields.

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