Combinatorial Foundation of Homology and Homotopy Applications to Spaces, Diagrams, Transformation Groups, Compactifications, Differential Algebras, Algebraic Theories, Simplicial Objects, and Resolutions |
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| Author:
| Baues, Hans-Joachim |
| Series title: | Springer Monographs in Mathematics Ser. |
| ISBN: | 978-3-642-08447-8 |
| Publication Date: | Dec 2010 |
| Publisher: | Springer
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| Book Format: | Paperback |
| List Price: | AUD $266.95 |
Book Description:
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In this book we consider deep and classical results of homotopy theory like the homological Whitehead theorem, the Hurewicz theorem, the finiteness obstruction theorem of Wall, the theorems on Whitehead torsion and simple homotopy equivalences, and we characterize axiomatically the assumptions under which such results hold. This leads to a new combinatorial foundation of homology and homotopy. Numerous explicit examples and applications in various fields of topology and algebra are given.
In this book we consider deep and classical results of homotopy theory like the homological Whitehead theorem, the Hurewicz theorem, the finiteness obstruction theorem of Wall, the theorems on Whitehead torsion and simple homotopy equivalences, and we characterize axiomatically the assumptions under which such results hold. This leads to a new combinatorial foundation of homology and homotopy. Numerous explicit examples and applications in various fields of topology and algebra are given.