Homotopy Theories and Model Categories
by W. G. Dwyer, J. Spalinski
Publisher: University of Notre Dame 1995
Number of pages: 56
This paper is an introduction to the theory of model categories, which was developed by Quillen. We have tried to minimize the prerequisites needed for understanding this paper; it should be enough to have some familiarity with CW-complexes, with chain complexes, and with the basic terminology associated with categories.
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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 Carlo Mazza, Vladimir Voevodsky, Charles Weibel - AMS
This book provides an account of the triangulated theory of motives. Its purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings.
by Andrew Ranicki, Norman Levitt, Frank Quinn - Springer
The book present original research on a wide range of topics in modern topology: the algebraic K-theory of spaces, the algebraic obstructions to surgery and finiteness, geometric and chain complexes, characteristic classes, and transformation groups.
by Daniel Dugger - University of Oregon
This is an expository paper on homotopy colimits and homotopy limits. These are constructions which should arguably be in the toolkit of every modern algebraic topologist. Many proofs are avoided, or perhaps just sketched.