Introduction to Topological Groups
by Dikran Dikranjan
Publisher: UCM 2007
Number of pages: 69
These notes provide a brief introduction to topological groups with a special emphasis on Pontryaginvan Kampen's duality theorem for locally compact abelian groups. We give a completely self-contained elementary proof of the theorem. According to the classical tradition, the structure theory of the locally compact abelian groups is built parallelly.
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The author discusses several exciting topological developments which radically changed the way we think about many issues. Topics covered: Poincare duality, Thom isomorphism, Euler, Chern and Pontryagin classes, cobordisms groups, signature formula.
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