Applications of Elliptic Operators and the Atiyah Singer Index Theorem
نویسنده
چکیده
1. Review of Differential Geometry 2 2. Definition of an Elliptic Operator 5 3. Properties of Elliptic Operators 7 4. Example of an Elliptic Operator 9 5. Example: The Euler Characteristic 12 6. Example: The Signature Invariant 14 7. A Theorem of Atiyah, Frank and Mayer 18 8. Clifford Algebras 20 9. A Diversion: Constructing Vector Fields on Spheres using Clifford Algebras 23 10. Topological Invariants of the Index. The Atiyah Singer Index Theorem 26 11. Borel Hirzebruch Theory and Characteristic Classes 30 12. Verification of the Index Theorem for Dχ 33 13. The Index of DS is the Hirzebruch L-genus 36 14. The Hirzebruch Riemann Roch Theorem 39 References 43
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