Description:

Singular homology, the de Rham cohomology (quantum mechanics on manifolds). The Čech cohomology and gauge fields. The Chevalley cohomology and projective representations in quantum theory. Deformations of associative and Lie algebras.

Contents:

1. - 3. Singular homology, de Rham cohomology. Quantum mechanics on manifolds.
4. - 6. Čech cohomology and gauge fields.
7.- 9. Cohomology of Lie algebras. Projective representations in quantum theory.
10. - 12. Deformations of associative and Lie algebras. Quantization as deformation of classical mechanics.

Recommended literature:

Key references:
[1]B.R. Pollard: An Introduction to Algebraic Topology, Bristol University, 1979

Recommended references:
[2] C. Nash: Topology and physics - a historical essay, arXiv: hep-th/9709135

Keywords:

singular homology, cohomology, associative algebra, Lie algebra, projective representation, deformations of algebras

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar