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 Peter Saveliev - Intelligent Perception
Differential forms provide a modern view of calculus. They also give you a start with algebraic topology in the sense that one can extract topological information about a manifold from its space of differential forms. It is called cohomology.
by J. S. Milne
These are the notes for a course taught at the University of Michigan in 1989 and 1998. The emphasis is on heuristic arguments rather than formal proofs and on varieties rather than schemes. The notes also discuss the proof of the Weil conjectures.
by Klaus Wirthmüller - Technische Universität Kaiserslautern
The purpose of this text is to make familiar with the basics of topology, to give a concise introduction to homotopy, and to make students familiar with homology. Readers are expected to have knowledge of analysis and linear algebra.
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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.