Topology for Physicists (T) - Topology
| Course | Topology for Physicists (T) |
|---|---|
| Course No. | Topology |
| Category | Type | Language | Teaching hours | CP | Semester |
|---|---|---|---|---|---|
| Elective | Lecture with exercises | English | 3+1 | 6 | ST |
Preparation: Bachelor of physics or mathematics; the basics of exterior calculus are assumed
Form of Testing and Examination: Written or oral examination
Length of Course: 1 semester
Aims of the Course: This course gives an introduction to various topological concepts and results that play an important role in modern theoretical physics.
Contents of the Course:
Elements of homotopy theory: homeomorphic spaces, homotopic maps, fundamental group, covering spaces, homotopy groups, long exact homotopy sequence of a fibration
Homology and cohomology: Poincare lemma, Mayer-Vietoris sequence, Cech-deRham complex, Hurewicz isomorphism theorem, spectral sequences
Vector bundles and characteristic classes: Euler form, Thom isomorphism, Chern classes
Applications: Berry phase; Dirac monopole problem; visualization of closed differential forms by Poincare duality; cohomology of electrical conductance; supersymmetry and Morse theory; index theorems; homotopy classification of topological insulators
Recommended Literature:
R. Bott and L.W. Tu: Differential forms in algebraic topology (Springer, 1982)
A.S. Schwarz, Topology for physicists (Springer, 1994)