Course  Materials  

Foliations, C* algebras and index theory
Part I of this course describes the classical approach to characteristic classes for foliations. This include the ChernWeil type construction, Bottâ€™s vanishing theorem, the GodbillonVey class, and the GelfandFuks cohomological realization. Part II is devoted to the noncommutative approach to characteristic classes of foliations, via transverse Hopf symmetry and Hopfcyclic cohomology. The main application discussed is the index theorem for transversely hypoelliptic operators on foliations. In part III Bott periodicity in its classical form and in its Banach algebra are discussed. An outline of characteristic classes leading to the AtiyahSinger formula are presented next. The AtiyahSinger formula is proved as a corollary of Bott periodicity. At the end, the index theorem for families of elliptic operators is developed. 
Part I, II
Henri Moscovici
Notes by P. Witkowski


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30.05.2005 

Table of contents  


Clarifications for the last lectures
Henri Moscovici


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19.07.2005 

Table of contents  


Part III
Paul Baum
Notes by P. Witkowski


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30.05.2005 

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Dirac operators and Spin structures
Paul Baum
Notes by P. Witkowski


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30.05.2005 

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Exam  Exam questions  

The exam was on 12th June 2005. It consisted of the written part (six exercises) and oral part. In the oral part each student had to answer two questions: easy one and difficult one (chosen from the two difficult questions). Three students (on the graduate and undergraduate level) passed the exam. 
Written part Oral part 