K-theory for C*-algebras, and beyond

Contact:
Serge Richard (richard@math.nagoya-u.ac.jp), Rm. 237 in Sci. Bldg. A

• Description : the pdf file

• Schedule : Friday 10.30 - 12.00 in room 552 of the Math Building
  

• Class dates :
  April 10, 17, 24
  May 1, 8, 15, 22, 29
  June 12, 19, 26
  July 3, 10, 17, 24
  

• Lecture notes : full document, 110 pages
  K-theory for C*-algebras, and beyond
  

• Lecture notes :
  Title
  Contents
  Chapter 1: C*-algebras
  Chapter 2: Projections and unitary elements
  Chapter 3: K_0-group for a unital C*-algebra
  Chapter 4: K_0-group for an arbitrary C*-algebra
  Chapter 5: The functor K_1
  Chapter 6: The index map
  Chapter 7: Higher K-functors, Bott periodicity
  Chapter 8: The six-term exact sequence
  Chapter 9: Cyclic cohomology
  Chapter 10: Application: Levinson's theorem
  Bibliography
  

• Student reports :
  Exercise 1.1.6 by Yuki Inoue
  K_1-groups and determinants by Kimura Seigo
  K-groups for complex matrices by Taro Uyeda
  Solutions to a few exercises by Tatsuya Hamada
  

• Additional material :
  Introduction: first lecture
  

• References : (electronic version available upon request)
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  [Con86] A. Connes, Cyclic cohomology and the transverse fundamental class of a foliation, in Geometric methods in operator algebras (Kyoto, 1983), 52--144, Pitman Res. Notes Math. Ser. 123, Longman Sci. Tech., Harlow, 1986.
  [Con94] A. Connes, Non-commutative geometry, Academic Press, Inc., San Diego, CA, 1994.
  [CMR07] J. Cuntz, R. Meyer, J. Rosenberg, Topological and bivariant K-theory, Oberwolfach Seminars, 36. Birkhauser Verlag, Basel, 2007.
  [GI03] V. Georgescu, A. Iftimovici, C*-algebras of quantum Hamiltonians, in Operator Algebras and Mathematical Physics, Conference Proceedings: Constanta (Romania) July 2001, 123-167, Theta Foundation, 2003.
  [GVF01] J. Gracia-Bondia, J Varilly, H. Figueroa, Elements of noncommutative geometry, Birkhauser Advanced Texts, Birkhauser Boston, Inc., Boston, MA, 2001.
  [Kha13] M. Khalkhali, Basic noncommutative geometry, EMS Series of Lectures in Mathematics. European Mathematical Society (EMS), Zürich, 2013.
  [KS04] J. Kellendonk, H. Schutz-Baldes, Boundary maps for C*-crossed products with R with an application to the quantum Hall effect, Comm. Math. Phys. 249 no. 3 (2004), 611-637.
  [MN08] H. Moriyoshi, T. Natsume, Operator algebras and geometry Translations of Mathematical Monographs 237, American Mathematical Society, Providence, RI, 2008.
  [Mur90] G.J. Murphy, C*-algebras and operator theory, Academic Press, Inc., Boston, MA, 1990.
  [Ped89] G. Pedersen, Analysis now, Graduate Texts in Mathematics, 118, Springer-Verlag, New York, 1989.
  [Ric15] S. Richard, Levinson's theorem: an index theorem in scattering theory, Proceedings of the Conference Spectral Theory and Mathematical Physics, Santiago 2014, Operator Theory Advances and Application, Birkhauser.
  [RLL00] M. Roerdam, F. Larsen, N. Laustsen, An introduction to K-theory for C*-algebras, London Mathematical Society Student Texts 49, Cambridge University Press, Cambridge, 2000.
  [Yos65] K. Yosida, Functional analysis, Die Grundlehren der Mathematischen Wissenschaften 123, Academic Press, Inc., New York; Springer-Verlag, Berlin 1965.
  [W-O93] N.E. Wegge-Olsen, K-theory and C*-algebras, a friendly approach, Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1993.