Avraham (Rami) Aizenbud

אברהם (רמי) איזנבוד

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ALGEBRAIC TOPOLOGY

AVRAHAM AIZENBUD

Lectures.

First term: Tuesday 11:15-13:00, Room 155; Second term: Tuesday 10:15-12:00, Room 155; .

T.A.

Shachar Carmenli - First term: Tuesday 16:15-18:00, Room 155; Second term: Monday 11:15-13:00, Room 155; .

Office hours.

by appointment..

Contents

1. General information

The course is of M.Sc. level. It includes some basic geometry facts every mathematician is expected to know. Math students are strongly recommended to attend, CS or physics students wishing to broaden their mathematical background are also welcome.

2. Overview

We will discuss homotopy and homology theory. The course is split into two units. The first one contains the most elementary facts of those theories, together with their detailed proofs. The second will contains more advanced material of both theories, The last lecture(s) will be an overview of more advance topics

3. Prerequisite

The students are expected to know basic general topology and group theory.

4. Chronological list of topics

See PDF file

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5. Textbooks

The literature for the course is [GHFFHAT]. All the material of the course (except some of the advance topics) appears in [HAT]. However, the order of the topics will be more similar to [GH] and [FF].

[GH] is the easiest one of the three, but it doesn’t cover all of the required information. [FF] contains most of what we will need, but omits too many details in some proofs. Additionally, [FF] is highly recommended for its illustrations.

[GH]    Greenberg and Harper, Algebraic topology: a first course.

[FF]    Fomenko and Fuks, Homotopic topology.

[HAT]    Hatcher, algebraic topology.

6. E-mail list

To join/un-join the course e-mail list send Shachar an e-mail (from the address you wish to join/un-join) with subject “join/un-join me to geom-5779”. To send a message to the course mailing list send Shachar an e-mail with subject “e-mail to geom-5779 – the subject of your message”.

7. How to get credit for the course?

The homework will be 100% of the grade. If you fill that you know some of the material well enough and you do not need to attend part of the course, you can come to me and convince me in that. If this is the case, you will be excused from the corresponding part of the homework, and accordingly the whight of the rest of the homework will increase.

The course is an year course, but the credit is separate for each term.

8. Lecture notes

9. Homework

1. The notes and the solutions are writen by the students, they might contain some mistakes. Students that wish to upload corrected versions are wellcome to send them to me.