Lecture notes for the course "Homological methods in
Non-commutative Geometry", Univ. of Tokyo, Oct. 2007-Mar.2008.
The lectures take place on Tuesdays, in the Graduate School of
Mathematics building (Komaba campus), rm. 128. I will be updating
this page as the course progresses. I hope to have the notes for
each lecture available before it starts. I will
occasionally rewrite earlier lectures, cf. changelog at the bottom
of the page. The notes are in PDF format. If you have any problem
with printing them out, or if you have any questions or comments on
the contents, please let me
know! If you are in Tokyo, you can also reach me at my office,
rm. 522 (I'm generally there at least after lunch, but to be sure,
perhaps it's better to make an appointment by e-mail).
Lecture 1 (16.10.07) [PDF]
Lecture 2 (30.10.07) [PDF]
Lecture 3 (06.11.07) [PDF]
Lecture 4 (13.11.07) [PDF]
Lecture 5 (20.11.07) [PDF]
Lecture 6 (27.11.07) [PDF]
Lecture 7 (10.12.07) [PDF]
Lecture 8 (08.01.08) [PDF]
Lecture 9 (15.01.08) [PDF]
Lecture 10 (22.01.08) [PDF]
Lecture 11 (29.01.08) [PDF]
Everything in a single file
Page last revised 12.03.08. Changelog:
- 12.03.08. Posted a concatenated version of the notes (with an
- 15.02.08. Posted the final edit of all the lectures (minor
changes, mostly just fixed the typos).
- 27.01.08. Rewrote Lecture 11 (added some proofs) and Lecture 10
(made some proofs more convincing). Also slightly rewrote Lecture 9
(added a necessary additional condition to Tamarkin's Theorem 9.8).
- 25.01.08. Posted Lecture 11.
- 21.01.08. Slightly rewrote Lecture 10. Also rewrote Lecture 9
(replaced "sketch of a part of a proof" of Proposition 9.4 with an
- 18.01.08. Posted Lecture 10.
- 10.01.08. Posted Lecture 9; slightly corrected Lecture 4 and
- 04.01.08. Posted Lecture 8; slightly changed the numbering of
equations in Lecture 1.
- 08.12.07. Corrected a semi-serious mistake in Lecture 6 (the
degeneration of the Hodge-to-de Rham spectral sequence in the group
algebra case is only true for the unity component of cyclic homology
with respect to the conjugacy classes decomposition). Posted Lecture
- 22.11.07. Made cosmetic changes to Lectures 4 and 5, posted
- 18.11.07. Found and fixed a mistake in Lecture 3 --
specifically, in part 3.4, which describes a "third bicomplex" for
cyclic homology; the end result is the same, but it only works in
characteristic 0. Made cosmetic changes to Lecture 4. Uploaded
- 11.11.07. Changed notation slightly in Lecture 3, posted Lecture
- 03.11.07. Rewrote Lecture 3 (made some corrections, added some
- 30.10.07. Corrected slightly Lecture 2, added some material, and
split it into two halves. Now Lecture 2 corresponds to the actual
lecture given, and the second half of the original text is Lecture
3. Lecture 3 is version 0.1, I will probably edit it further.
- 28.10.07. Added some material to Lecture 1 (now it corresponds
more closely to the actual lecture), posted Lecture 2, made up
this title page.
- 15.10.07. Posted Lecture 1.
Offtopic: here are the slides of my talk at
A. Fujiki's 60th anniversary conference in Osaka, Nov. 1- Nov. 5
2007. This is seriously "work in progress", some "theorems" have not
been written down yet -- use at your own risk.