Avraham (Rami) Aizenbud 
אברהם (רמי) איזנבוד 










ALGEBRAIC TOPOLOGY
Tuesday 12:1514:00, Room 261.
Tuesday 14:1515:00, Room 122. If you would like to come to the oﬃce hours or at some other time please email me. Contents 1. General
information
2. Overview 3. Prerequisite 4. Chronological list of topics 5. Textbooks 6. Email list 7. How to get credit for the course? 8. Lecture notes 9. Homework 1. General informationThe course is part of the course “Basic topics in geometry 1”. The second part “Analysis on manifold” by Dmitry Novikov. The two parts will depend on each other and the students are expected to attend both parts (unless they know the material of one of them). 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. OverviewWe 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, with sometimes more sketchy proofs. The last lecture will be an overview of more advance topics 3. PrerequisiteThe students are expected to know basic general topology and group theory. 4. Chronological list of topics4.1. Basic Homotopy theory.
4.2. Basic Homology theory.
4.4. Advanced Homology theory.
5. TextbooksThe literature for the course is [GH, FF, HAT]. The course will follow a “convex combination” of [GH] and [FF]. We will use [HAT] as a source of examples, problems and additional information. [GH] is the easiest one of the three, but it doesn’t cover all of the required information. [FF] contains almost everything we will need, but omits too many details in some proofs. Also, the order of the topics in the course will be something between [GH] and [FF]. Additionally, [FF] is highly recommended for its illustrations. Finally, [HAT] is the most detailed of these three books, but it is too big to serve as a textbook for a ﬁrst course in algebraic topology. [GH] Greenberg and Harper, Algebraic topology: a ﬁrst course. [FF] Fomenko and Fuks, Homotopic topology. [HAT] Hatcher, algebraic topology. 6. Email listTo join/unjoin the course email list send me an email (from the address you wish to join/unjoin) with subject “join/unjoin me to geom5775”. To send a message to the course mailing list send me an email with subject “email to geom5775 – the subject of your message”. 7. How to get credit for the course?The homework will be 30% of the grade and the ﬁnal exam 70%. If you ﬁll that you know same 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 wight of the exam will increase. 8. Lecture notes9. HomeworkHomework 2, Solution a, Solution b Homework 5, Solution a, Solution b Homework 6, Solution a, , Solution b Homework 7, Solution a, Solution b Homework 9, Solution a, Solution b 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. 