Seminar on K-theory

• syllabus.pdf

Text:

• J. Milnor: Introduction to algebraic K-theory, Annals of Mathematics Studies, No. 72, Princeton University Press, Princeton, N.J., University of Tokyo Press, Tokyo, 1971.
• M. F. Atiyah: K-theory. Lecture notes by D. W. Anderson, W. A. Benjamin, Inc., New York-Amsterdam, 1967.
• C. A. Weibel: An introduction to algebraic K-theory, available for free download here.

Time and place: Friday 1-2:30 in Science Bldg. 1, room 455.

Schedule:

• April 15: Introduction. (Hesselholt)
• April 22: The Grothendieck group K₀(Λ). (Mitani)
• May 1: The Grothendieck group and ideal class group of a Dedekind domain. (Ogawara)
• May 8: The ring of integers in a number field is a Dedekind domain. (Ogawara)
• May 13: Milnor squares. (Sugiyama)
• May 20: The Whitehead group K₁(Λ). (Sone)
• May 29: The exact sequence associated with a Milnor square. (Saito)
• June 19: The exact sequence associated with an ideal. (Mitani)
• June 24: Vector bundles and projective modules. (Ogawara)
• June 26: Swan's theorem. (Ogawara)
• July 1: Topological K-theory. (Sugiyama)
• July 8: Grassmann manifolds. (Sone)
• July 15: G-bundles over G-spaces. (Mitani)
• July 22: The Bott periodicity theorem. (Saito)
• July 15: Cartan-Eilenberg systems and spectral sequences. (Ogawara)
• October 7: No class.
• October 16: Cartan-Eilenberg systems and multiplicative spectral sequences. (Ogawara)
• October 23: Quillen (co)homology. (Sugiyama)
• October 30: Quillen (co)homology, continued. (Sugiyama)
• November 6: Witt vectors and λ-rings. (Sone)
• November 20: Witt vectors and λ-rings, continued. (Sone)
• November 27: Adams operations and the Hopf invariant one problem. (Saito)
• December 4: Ext-groups. (Mitani)
• December 11: Singular homology. (Saito)
• December 18: The Steenrod algebra. (Ogawara)
• January 8: The Steenrod algebra, continued. (Ogawara)
• January 15: The structure of the dual Steenrod algebra. (Saito)
• January 22: The Adams-Novikov spectral sequence. (Hesselholt)