ELEMENTS OF GEOMETRY (CLASSICAL AND QUANTUM)
by L. Dabrowski, SISSA
This introductive course (20 hours ca.) is meant as a
`piecewise continuous' journey through few selected aspects
of geometry of a `classical' space X in terms of
(commutative) algebra of functions A =
F(X). In particular, Riemannian structure will be
encoded by means of Dirac operator. Possible
generalizations to noncommutative algebra A will be briefly
indicated.
Proposed topics:
- Clifford algebras, spinorial and orthogonal groups
- Spinors, charge conjugation
- Spin structures and spinor fields
- Dirac operator
- Connes `reconstruction' theorem
- quantum
- groups (Hopf algebras)
- topology (C*-algebras)
- vector bundles (projective modules)
- principal bundles (Hopf-Galois extensions)
- differential calculus, connections and Dirac operator
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