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Chern–Weil Theory Extended to a Class of Infinite Dimensional Bundles

Hesari, Abdolaziz | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45726 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Esfahani Zadeh, Mostafa
  7. Abstract:
  8. Given a principal bundle a characteristic class is an element of the cohomology al- gebra of the classifying space of structure group of the bundle with coefficients in a commutative ring with unit ,which have a functorial property .When the structure groupe of the bundle is a Lie group and the coefficient ring is the real or complex num- bers , the Chern–Weil approach provides a geometric construction of char-acteristic classes. Classical Chern–Weil formalism relates geometry to topology, assigning to the cur- vature of a connection, de Rham cohomology classes of the underlying manifold.This theory developped in the 40’s by Shiing-ShenChern and Andre Weil which can be seen as a generalisation of the Chern-Gauss-Bonnet Theorem .In this thesis we extended the classical Chern–Weil formalism to an infinite n-sional setup using regularised traces on classical pseudodifferential operators
  9. Keywords:
  10. Pseudo Differential Operator ; Infinite Dimensional Manifolds ; Wadzicki Trace ; Leading Symbol Theory ; Chern-Weil Theory

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