Math 691 (Phillips)
This is the home page for N. C. Phillips'
Math 691 at the University of Oregon, winter quarter 2023.
Course information

Course number:
Math 691.

Course title: Topics in Ktheory.

CRN: 23184.

UO
class schedule page for this course.

Instructor: N. Christopher
Phillips.

Office: 105 Deady [now renamed to "University Hall"].
Please knock.
I can't leave my door open, because if I do I get too many people
asking to borrow my stapler or pencil sharpener, or
where to find the math department office
or nonexistent rooms (such as 350 Deady).

Office hours: Mondays 1:00 am2:00 pm [except during the first three
weeks of classes], Tuesdays 11:00 am12:00 noon and 3:004:00 pm,
or by
appointment.

Email.
All messages should have a subject starting "Math 691:".
Binary files or attachments are accepted only by prior arrangement.
I do not ever accept
Microsoft Word documents, html (web) files, or encoded text messages.
Please send 7 bit ASCII plain text only.

Time and place: MWF 11:0011:50 am,
room 205 Deady [now renamed to "University Hall"].

Textbook: M. F. Atiyah, KTheory.
Electronic
copy supposedly available.
(This has not been checked.)

Prerequisites:
Math 634636; in principle also Math 690.
Eventually some basic knowledge of smooth manifolds will be needed.
Course description
Modified course description
The description below was originally written for a course starting
Ktheory for the beginning.
However, Boris Botvinnik's Math 690 in Fall 2022 covered a
substantial amount of Ktheory.
(I have not found a website for this course.)
Therefore some topics on the list below will be reviewed only
very briefly,
and other topics, not on the list, will be covered in the course.
Since some students are expected who did not have Math 690,
the course will begin with a fast paced review from the beginning,
with the opportunity to ask questions.
In particular, items (1) and (2) on the list below were done,
while items (3) (Bott periodicity) was not, and will be treated
carefully in this course.
Original course description
Outline of topics:

Vector bundles.

Vector bundles over compact spaces.

Bott periodicity.

Ktheory as a cohomology theory.

Products in Ktheory.

The Thom isomorphism and computations of Ktheory in other examples.

Pseudodifferential operators and the calculus of symbols.

Application to the Hopf invariant problem..
This is a course on the Ktheory of (locally) compact Hausdorff spaces,
not on the Ktheory of C*algebras. C*algebras will be mentioned only
occasionally, and no knowledge of them (or interest in them) is assumed.
Nevertheless, this course is important background for anyone interested
in the Ktheory of C*algebras.
This course contains much of the algebraic topological background
relevant to this year's Math 684685 sequence on elliptic
pseudodifferential operators, the analysis background for the
AtiyahSinger Index Theorem. Taking this course will not be necessary
for Math 684685: the material needed there will be summarized there.
Course files
See the
comments
on the different formats
for more information on the formats of files posted below.
One warning is important enough to give here: In the winter quarter 1998,
somebody printed some of my pdf files
somewhere on campus and found that certain mathematical symbols
(such as minus signs in exponents) did not print, damaging the meanings.
This page maintained by
N. Christopher Phillips,
email.
When emailing me, please use 7 bit ASCII plain text only.
In particular:

No binary files or attachments (except by prior arrangement).

No Microsoft Word files.
I do not accept these under any circumstances,
since I don't have software that reads them.
If you really want to send something in a word processor format,
use TeX.

No html encoded messages.

No mime encoding or other encoding of ordinary text messages.
Last significant change 7 January 2023.