Combinatorial Foundation of Homology and Homotopy Applications to Spaces, Diagrams, Transformation Groups, Compactifications, Differential Algebras, Algebraic Theories, Simplicial Objects, and Resolutions

This book considers 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 characterizes axiomatically the assumptions under which...

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Main Author: Baues, Hans-Joachim
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1999, 1999
Series:Springer Monographs in Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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245 0 0 |a Combinatorial Foundation of Homology and Homotopy  |h Elektronische Ressource  |b Applications to Spaces, Diagrams, Transformation Groups, Compactifications, Differential Algebras, Algebraic Theories, Simplicial Objects, and Resolutions  |c by Hans-Joachim Baues 
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505 0 |a Examples and Applications in Topological Categories -- B: Examples and Applications in Algebraic Homotopy Theories -- C: Applications and Examples in Delicate Homotopy Theories of Simplicial Objects -- D: Resolutions in Model Categories -- II. Combinatorial Homology and Homotopy -- I: Theories of Coactions and Homology -- II: Twisted Chain Complexes and Twisted Homology -- III: Basic Concepts of Homotopy Theory -- IV: Complexes in Cofibration Categories -- V: Homology of Complexes -- V: Homology of Complexes -- VII: Finiteness Obstructions -- VIII: Non-Reduced Complexes and Whitehead Torsion -- List of Notations 
653 |a Mathematics 
653 |a K-theory 
653 |a Algebraic topology 
653 |a Mathematics 
653 |a Algebraic Topology 
653 |a K-Theory 
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520 |a This book considers 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 characterizes 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