MTH546: Cohomology

Note: If this course is being taught this semester, more information can be found at the course home page.

Cross Listed

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Prerequisites

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This course is a prerequisite or co-requisite for

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Description

This course introduces and studies the cohomology of groups and its applications in topology, geometry and number theory.

Cohomology of groups helps provide quantitative information on groups and the objects they act upon. Among the topics covered are:

  1. Tate cohomology of finite groups. Classification of groups that act freely on spheres.

  2. Group actions on spaces. Equivariant cohomology and Smith Theory of p-group actions.

  3. Serre’s construction and cohomological dimension. Hattori-Stallings rank of finitely generated projective modules. Euler characteristics of arithmetic groups and special values of zeta functions.

  4. Profinite groups and continuous group cohomology. Galois cohomology and the Brauer group. Low dimensional cohomology with nonabelian coefficients and basic applications to Galois theory.

Topics covered

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