Lectures on Introduction to Algebraic Topology
by G. de Rham
Publisher: Tata Institute of Fundamental Research 1969
Number of pages: 71
These are notes of a part of lectures which the author gave at the Tata Institute of Fundamental Research in 1966. They were intended as a first introduction to algebraic Topology. Contents: Definition and general properties of the fundamental group; Free products of groups and their quotients; On calculation of fundamental groups; The group of a tame link given by a good plane projection; etc.
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by Dikran Dikranjan - UCM
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.
by Boris Botvinnik - University of Oregon
Contents: Important examples of topological spaces; Constructions; Homotopy and homotopy equivalence; CW-complexes and homotopy; Fundamental group; Covering spaces; Higher homotopy groups; Fiber bundles; Suspension Theorem and Whitehead product; etc.
by D. G. Bourgin - Macmillan
Contents: Preliminary algebraic background; Chain relationships; The absolute homology groups and basic examples; Relative omology modules; Manifolds and fixed cells; Omology exact sequences; Simplicial methods and inverse and direct limits; etc.
by J. P. May - Springer
The theme of this book is infinite loop space theory and its multiplicative elaboration. The main goal is a complete analysis of the relationship between the classifying spaces of geometric topology and the infinite loop spaces of algebraic K-theory.