Pontryagin Duality and the Structure of Locally Compact Abelian Groups

These lecture notes begin with an introduction to topological groups.

Sidney A. Morris (Author)

9780521215435, Cambridge University Press

Paperback, published 4 August 1977

140 pages
22.8 x 15.2 x 2.2 cm, 0.55 kg

These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses.

1. Introduction to topological groups
2. Subgroups and quotient groups of Rn
3. Uniform spaces and dual groups
4. Introduction to the Pontryagin-van Kampen duality theorem
5. Duality for compact and discrete groups
6. The duality theorem and the principal structure theorem
7. Consequences of the duality theorem
8. Locally Euclidean and NSS-groups
9. Non-abelian groups.

Subject Areas: Algebra [PBF]