# Spectral Sequences

#### Hilary Term 2011. Class TR11-12 in SGSR1; office hours R14-15 in SGS7

##### Course description

The course will cover: motivations for and the structure of spectral sequences; computational techniques for working with spectral sequences; methods for constructing spectral sequences, including filtered complexes and exact couples; examples of spectral sequences, including the Mayer-Vietoris SS, Serre SSs, the Atiyah-Hirzebruch SS, Eilenberg-Moore SSs, and the Bockstein SS; Steenrod operations and Massey products in spectral sequences; and applications to computations of homology of Lie groups, classifying spaces, and homogeneous spaces, and homotopy groups of spheres, among other topics.

The natural prerequisite is a working knowledge of basic homological algebra, though references will be provided to help students fill in any needed background material. The course will be highly participatory, and weekly problem sheets will be an important basis for discussion and student involvement. Needless to say, students and others in geometry, representation theory, algebra, and other disciplines, are all welcome. Though in tone the course will be aimed at graduate students, the content may well be of interest to postdocs and faculty as well.

##### Syllabus and problem sheets

The syllabus contains a page of references and resources. The problem sheets will be distributed each Thursday, for discussion in class the following Thursday.

##### Contact information

Christopher Douglas

Office: SGS7

Email: cdouglas at maths