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Infinite Homotopy Theory (K-Monographs in Mathematics, Volume 6)
Rok: 2001
ISBN: 9780792369820
OKCZID: 110108673
Citace (dle ČSN ISO 690):
BAUES, Hans J. Infinite homotopy theory. Dordrecht: Kluwer Academic Publishers, c2001. vii, 296 s. K-monographs in mathematics, v. 6.
Anotace
This book deals with algebraic topology, homotopy theory and simple homotopy theory of infinite CW-complexes with ends. Contrary to most other works on these subjects, the current volume does not use inverse systems to treat these topics. Here, the homotopy theory is approached without the rather sophisticated notion of pro-category. Spaces with ends are studied only by using appropriate constructions such as 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 will be of interest to researchers whose work involves algebraic topology, category theory, homological algebra, general topology, manifolds, and cell complexes.