Syllabus - Spring, 2002

** Part I. The algebraic theory of spinors.**

(i) Clifford algebras: structure and representation theory.

(ii) Spin groups and spinor representations.

** Part II. K-Theory and characteristic classes.**

(i) -theory and -theory.

(ii) Classifying spaces and characteristic classes.

(iii) Bott Periodicity and the relationship to Clifford algebras.

** Part III. Spin-manifolds and Spin-manifolds.**

(i) Spin-manifolds - definitions and examples.

(ii) Spin-manifolds - definitions and examples.

(iii) Spin-cobordism.

** Part IV. Spinor bundles, connections and Dirac operators.**

(i) Clifford and Spinor bundles.

(ii) The Levi-Civita connection on spinors.

(iii) Construction of the Dirac operators.

** Part V. The Atiyah-Singer Index Theorem.**

(i) The index theorem.

(ii) The index theorem for families.

(iii) The C-index theorem.

** Part VI. Applications to geometry and topology.**