Homotopy Theory
August- November 2015

Click here for the homeworks.
Lectures: Mondays and Tuesdays from 2 to 3:15 pm
Classroom: Lecture Hall 2
Instructor: Priyavrat Deshpande.
Contact: Office: 403
phone: 962
email: pdeshpande AT cmi DOT ac DOT in
Office Hours:
 Wednesdays from 11:30 to 12:30
Teaching Assistant: TBA
Useful reading material:
  • Lecture Notes in Algebraic Topology by James F. Davis and Paul Kirk, AMS, GSM 35.
  • Algebraic Topology Homology and Homotopy by Robert Switzer, Springer-Verlag.
  • Lectures on Algebraic Topology, Albrecht Dold, Springer-Verlag.
Prerequisites:   Knowledge of (co)homology theory (graduate course in algebraic topology) and/or permission from the faculty advisor.
  • Homework 40%
  • Project report 30%
  • Presentation 30%
Web: http://www.cmi.ac.in/~pdeshpande/ttop15.html

Course syllabus
  1. Homotopy groups.
  2. Fiber bundles, Serre spectral sequence and homotopy groups of spheres.
  3. Localization and an introduction to rational homotopy theory.


The homework will be assigned in class (bi-monthly). It is your duty to submit the solutions on time. Copying and/or plagiarism will not be tolerated. Here are a few writing guidelines you might want to follow.
  1. Feel free to work together, but you should submit your own work.
  2. Your questions/comments/suggestions are most welcome. I will also be fairly generous with the hints. However, do not expect any kind of help, including extensions, on the day a homework is due.
  3. Please turn in a neat stapled stack of papers. Refrain from using blank / printing paper. Use ruled paper.
  4. Your final finished version should be as polished as you can make it. This probably means that you cannot submit sketchy solutions or sloppily written first versions. Please expect to do a fair amount of rewriting. Do not hand in work with parts crossed out; either use a pencil and erase or rewrite.
  5. Please write complete sentences that form paragraphs and so forth. It might be a good idea to use short simple sentences; avoid long complicated sentences.
  6. Do use commonly accepted notation (e.g., for functions, sets, etc.) and never invent new notation when there is already some available.
  7. Make sure you provide a statement clearly indicating precisely what it is that you are about to prove. You can, if you want, label your statement as a Theorem or Claim or whatever. Write the word Proof, and then give your proof.
  8. Throughout your writing, constantly tell the reader (i.e. me, :-)) exactly what it is that you are about to demonstrate. Be sure to indicate the end of your proof.
  9. Your answers should combine “logic”, your hypotheses, and possibly other mathematical facts (e.g., theorems that we have proved in class) into an argument that establishes the asserted conclusion.
  10. Please be extra careful about the order in which you use your quantifiers.
  11. In your arguments you can make free use of anything that we have proven in class, and of course all logic rules and basic axioms and definitions. Anything else that you use should be proved.


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