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Combinatorial Foundation of Homology and Homotopy: Applications of Spaces, Diagrams, Transformation groups, Compactifications, Differential Algebras, Algebraic Theories, Simplical Objects, and Resolutions

Monograph

By: HJ Baues

Springer-Verlag

Hardback | Dec 1999 | #97632 | ISBN: 3540649840
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NHBS Price: £108.00 $138/€129 approx

About this book

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.


Contents

Preface.- Leitfaden.- Fields of application.- Theories of coactions and homology.- Twisted chain complexes and twisted homology.- Basic concepts of homotopy theory.- Complexes in cofibration categories.- Homology of complexes.- Realization of chain maps.- Finiteness obstructions.- Non-reduced complexes and Whitehead torsion.- Literature.

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