Overview

This text deals with algebraic topology, homotopy theory and simple homotopy theory of infinite CW-complexes with ends. The homotopy theory is approached without the rather sophisticated notion of pro-category. Spaces spherical objects of CW-complexes in the category of spaces with ends, and all arguments refer directly to this category. In this way, infinite homotopy theory is presented as a natural extension of classical homotopy theory. In particular, this book introduces the construction of the proper groupoid of a space with ends and then the cohomology with local coefficients is defined by the enveloping ringoid of the proper fundamental groupoid. This volume should be of interest to researchers whose work involves algebraic topology, category theory, homological algebra, general topology, manifolds, and cell complexes.

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9780792369820

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Reviews

From the reviews: In this book the authors try to deal with more general spaces in a fundamental way by setting up algebraic topology in an abstract categorical context which encompasses not only the usual category of topological spaces and continuous maps, but also several categories related to proper maps. ... all concepts are carefully explained and detailed references for the proofs are given. ... a good understanding of the basics of ordinary homotopy theory is all that is needed to enjoy reading this book. (F. Clauwens, Nieuw Archief voor Wiskunde, Vol. 7 (2), 2006)

From the reviews: <p> In this book the authors try to deal with more general spaces in a fundamental way by setting up algebraic topology in an abstract categorical context which encompasses not only the usual category of topological spaces and continuous maps, but also several categories related to proper maps. a ] all concepts are carefully explained and detailed references for the proofs are given. a ] a good understanding of the basics of ordinary homotopy theory is all that is needed to enjoy reading this book. (F. Clauwens, Nieuw Archief voor Wiskunde, Vol. 7 (2), 2006)

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