Infinite Homotopy Theory

By A. Quintero and Hans-Joachim Baues

Book Overview

Compactness in topology and finite generation in algebra are nice properties to start with. However, the study of compact spaces leads naturally to non-compact spaces and infinitely generated chain complexes; a classical example is the theory of covering spaces. In handling non-compact spaces we must take into account the infinity behaviour of such spaces. This necessitates modifying the usual topological and algebraic cate- gories to obtain "proper" categories in which objects are equipped with a "topologized infinity" and in which morphisms are compatible with the topology at infinity. The origins of proper (topological) category theory go back to 1923, when Kere- kjart6 [VT] established the classification of non-compact surfaces by adding to orien- tability and genus a new invariant, consisting of a set of "ideal points" at infinity. Later, Freudenthal [ETR] gave a rigorous treatment of the topology of "ideal points" by introducing the space of "ends" of a non-compact space. In spite of its early ap- pearance, proper category theory was not recognized as a distinct area of topology until the late 1960's with the work of Siebenmann [OFB], [IS], [DES] on non-compact manifolds.

• Format: Paperback
• Language: English
• ISBN: 9401064938
• ISBN13: 9789401064934
• Release Date: October 2013
• Publisher: Springer
• Length: 296 Pages
• Weight: 0.96 lbs.
• Dimensions: 0.7" x 6.1" x 9.2"