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Differentiable structures definition and classification - Lec 07 - Frederic Schuller
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Classroom Contents
Geometrical Anatomy of Theoretical Physics
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- 1 Introduction/Logic of propositions and predicates- 01 - Frederic Schuller
- 2 Axioms of set Theory - Lec 02 - Frederic Schuller
- 3 Classification of sets - Lec 03 - Frederic Schuller
- 4 Topological spaces - construction and purpose - Lec 04 - Frederic Schuller
- 5 Topological spaces - some heavily used invariants - Lec 05 - Frederic Schuller
- 6 Topological manifolds and manifold bundles- Lec 06 - Frederic Schuller
- 7 Differentiable structures definition and classification - Lec 07 - Frederic Schuller
- 8 Tensor space theory I: over a field - Lec 08 - Frederic P Schuller
- 9 Differential structures: the pivotal concept of tangent vector spaces - Lec 09 - Frederic Schuller
- 10 Construction of the tangent bundle - Lec 10 - Frederic Schuller
- 11 Tensor space theory II: over a ring - Lec 11 - Frederic Schuller
- 12 Grassmann algebra and deRham cohomology - Lec 12 - Frederic Schuller
- 13 Lie groups and their Lie algebras - Lec 13 - Frederic Schuller
- 14 Classification of Lie algebras and Dynkin diagrams - Lec 14 - Frederic Schuller
- 15 The Lie group SL(2,C) and its Lie algebra sl(2,C) - lec 15 - Frederic Schuller
- 16 Dynkin diagrams from Lie algebras, and vice versa - Lec 16 - Frederic Schuller
- 17 Representation theory of Lie groups and Lie algebras - Lec 17 - Frederic Schuller
- 18 Reconstruction of a Lie group from its algebra - Lec 18 - Frederic Schuller
- 19 Principal fibre bundles - Lec 19 - Frederic Schuller
- 20 Associated fibre bundles - Lec 20 - Frederic Schuller
- 21 Conncections and connection 1-forms - Lec 21 - Frederic Schuller
- 22 Local representations of a connection on the base manifold: Yang-Mills fields - Lec 22
- 23 Parallel transport - Lec 23 - Frederic Schuller
- 24 Curvature and torsion on principal bundles - Lec 24 - Frederic Schuller
- 25 Covariant derivatives - Lec 25 - Frederic Schuller
- 26 Application: Quantum mechanics on curved spaces - Lec 26 - Frederic Schuller
- 27 Application: Spin structures - lec 27 - Frederic Schuller
- 28 Application: Kinematical and dynamical symmetries - Lec 28 - Frederic Schuller
