Daniel A. Ramras

 

 


Homework and Lecture Notes for Math 643: Spectral Sequences in Algebraic Topology


Homework 1

Homework 2

Homework 3

Homework 4


Lecture notes:

Lecture 1: Higher Homotopy Groups


Lecture 2: Fibrations


Lecture 3: Examples of Fibrations


Lecture 4: Towers of Fibrations and Spectral Sequences


Lecture 5: The Spectral Sequence of a 3-term Filtration


Lectures 6 and 7: The Spectral Sequence of a Filtered Complex and the Serre Spectral Sequence


Lecture 8: Examples: The Cellular Chain Complex and the Unitary Groups.


Lecture 9: The E^2 term of the Serre Spectral Sequence.


Lectures 10-11: Further examples and applications of the Serre Spectral Sequence.


Lecture 12: Cohomology.


Lectures 13-14: The Serre Spectral Sequence for cohomology and applications.


Lecture 15: Vector bundles and K-theory.


Lectures 16-17: Cohomology theories and the Atiyah-Hirzebruch Spectral Sequence.


Notes on principal bundles: These are notes (from a previous course) covering the classification of principal bundles, which will be needed for the proof of Bott Periodicity.


Lecture 18: The classification of principal U(n)-bundles. (A condensed version of the above notes.)


Lecture 19: The cohomology of BU.


Lectures 20-21: The Bott map and the homology of SU(n).


Lectures 22-23: Conclusion to the proof of Bott Periodicity.