Daniel A. Ramras 


Lecture notes:
Lecture 2: Fibrations Lecture 3: Examples of Fibrations Lecture 4: Towers of Fibrations and Spectral Sequences Lecture 5: The Spectral Sequence of a 3term 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 1011: Further examples and applications of the Serre Spectral Sequence. Lecture 12: Cohomology. Lectures 1314: The Serre Spectral Sequence for cohomology and applications. Lecture 15: Vector bundles and Ktheory. Lectures 1617: Cohomology theories and the AtiyahHirzebruch 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 2021: The Bott map and the homology of SU(n). Lectures 2223: Conclusion to the proof of Bott Periodicity. 