Combinatorial Foundation of Homology and Homotopy
Applications to Spaces, Diagrams, Transformation Groups, Compactifications, Differential Algebras, Algebraic Theories, Simplicial Objects, and Resolutions
Published on 27. November 1998
Book
Hardback
XV, 365 pages
978-3-540-64984-7 (ISBN)
Description
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.
More details
Series
Edition
1999 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XV, 365 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 26 mm
Weight
752 gr
ISBN-13
978-3-540-64984-7 (9783540649847)
DOI
10.1007/978-3-662-11338-7
Schweitzer Classification
Other editions
Additional editions
Hans-Joachim Baues
Combinatorial Foundation of Homology and Homotopy
Applications to Spaces, Diagrams, Transformation Groups, Compactifications, Differential Algebras, Algebraic Theories, Simplicial Objects, and Resolutions
Book
12/2010
Springer
€106.99
Shipment within 7-9 days
Content
I. Examples and Applications.- 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.