A Topology Primer
by Klaus Wirthmüller
Publisher: Technische Universität Kaiserslautern 2002
Number of pages: 197
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 successfully completed their first year courses in analysis and linear algebra.
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by Peter Petersen - UCLA
These notes are a supplement to a first year graduate course in manifold theory. These are the topics covered: Manifolds (Smooth Manifolds, Projective Space, Matrix Spaces); Basic Tensor Analysis; Basic Cohomology Theory; Characteristic Classes.
by Greg Friedman - arXiv.org
This is an introduction to simplicial sets and simplicial homotopy theory with a focus on the combinatorial aspects of the theory and their geometric/topological origins. Accessible to students familiar with the fundamentals of algebraic topology.
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 Paul Goerss - Northwestern University
Contents: The Adams spectral sequence; Classical calculations; The Adams-Novikov Spectral Sequence; Complex oriented homology theories; The height filtration; The chromatic decomposition; Change of rings; The Morava stabilizer group.