Combinatorial Foundation Of Homology And Homotopy Applications To Spaces Diagrams Transformation Groups Compactifications Differential Algebras Algebraic Theories Simplicial Objects And Resolutions
Publisher: Springer
Published: 2010
Number of pages: 365
ISBN-13: 9783642084478
Description: 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.