Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, V. Topological Spaces: Some Heavily Used Invariants

In This Lecture Course

• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, I. Introduction/Logic of Propositions and Predicates
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, II. Axioms of Set Theory
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, III. Classification of Sets
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, IV. Topological spaces: Construction and Purpose
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, V. Topological Spaces: Some Heavily Used Invariants
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, VI. Topological Manifolds and Manifold Bundles
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, VII. Differential Structures: Definition and Classification
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, VIII. Tensor Space Theory I: Over a Field
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, IX. Differential Structures: the Pivotal Concept of Tangent Vector Spaces
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, X. Construction of the Tangent Bundle
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XI. Tensor Space Theory II: Over a Ring
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XII. Grassmann Algebra and de Rham Cohomology
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XIII. Lie Groups and Their Lie Algebras
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XIV. Classification of Lie Algebras and Dynkin Diagrams
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XV. The Lie Group SL₂(ℂ) and its Lie Algebra 𝔰𝔩₂(ℂ)
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XVI. Dynkin Diagrams from Lie Algebras, and Vice Versa
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XVII. Representation Theory of Lie Groups and Lie Algebras
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XVIII. Reconstruction of a Lie Group from its Algebra
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XIX. Principal Fibre Bundles
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XX. Associated Fibre Bundles
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XXI. Connections and Connection 1-Forms
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XXII. Local Representations of a Connection on the Base Manifold: Yang-Mills Fields
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XXIII. Parallel Transport
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XXIV. Curvature and Torsion on Principal Bundles
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XXV. Covariant derivatives
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XXVI. Application: Quantum Mechanics on Curved Spaces
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XXVII. Application: Spin Structures
• Frederic Schuller: Lectures on Geometrical Anatomy of Theoretical Physics, XXVIII. Application: Kinematical and Dynamical Symmetries