Combinatorial Foundation of Homology and Homotopy: Applications to Spaces, Diagrams, Transformation Groups, Compactifications, Differential Algebras, Algebraic Theories, Simplicial Objects, and ResolutionsSpringer Science & Business Media, 9 mar 2013 - 365 páginas 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. |
Índice
3 | |
18 | 45 |
Examples and Applications | 51 |
Applications and Examples | 71 |
34 | 84 |
Quillen Model Categories | 98 |
4 | 110 |
Theories of Coactions and Homology | 129 |
The Homological Whitehead Theorem | 286 |
The Model Lifting Property of the Twisted Chain Functor | 287 |
Obstructions for the Realizability of Twisted Chain Complexes | 291 |
The Hurewicz Theorem | 294 |
EilenbergMac Lane Complexes and C THomology of Coefficient Objects | 296 |
Finiteness Obstructions | 301 |
The Finiteness Obstruction Theorem | 303 |
Finiteness Obstructions for Twisted Chain Complexes | 304 |
Twisted Chain Complexes and Twisted Homology | 169 |
4 | 198 |
Homotopy Cogroups and Homotopy Coactions | 207 |
8 | 220 |
Filtered Objects | 229 |
Complexes in Cofibration Categories | 246 |
Homology of Complexes | 249 |
The Chains of a Complex | 254 |
The Homology of a Complex | 257 |
The Obstruction Cocycle | 260 |
The Hurewicz Homomorphism and Whiteheads Exact Sequence | 262 |
Homology of Complexes | 267 |
Obstructions for the Realizability of Chain Maps | 271 |
The Homotopy Lifting Property of the Chain Functor | 276 |
Counting Realization of Chain Maps | 277 |
Linear Extensions and Towers of Categories | 279 |
The Homological Tower of Categories | 283 |
Proof of the Finiteness Obstruction Theorem | 312 |
NonReduced Complexes and Whitehead Torsion 315 | 314 |
Cells in a Cofibration Category | 317 |
NonReduced Complexes | 319 |
The Ball Pair Axiom | 323 |
Cellular ICategories | 327 |
Elementary Expansions | 328 |
Formal Deformations and Simple Homotopy Equivalences | 330 |
The Whitehead Group and Whitehead Torsion | 334 |
Simplified Form of Elements in the Whitehead Group | 339 |
The Torsion Group K₁ | 343 |
The Algebraic Whitehead Group | 344 |
The Isomorphism Between the Geometric and Algebraic Whitehead Group | 345 |
355 | |
361 | |
Otras ediciones - Ver todo
Combinatorial Foundation of Homology and Homotopy: Applications to Spaces ... Hans-Joachim Baues Vista previa restringida - 1998 |
Combinatorial Foundation of Homology and Homotopy Hans-Joachim Baues No hay ninguna vista previa disponible - 2014 |
Combinatorial Foundation of Homology and Homotopy: Applications to Spaces ... Hans-Joachim Baues No hay ninguna vista previa disponible - 2010 |
Términos y frases comunes
1-homotopy A-finite abelian groups additive category An+1 attaching map Baues AH bijective carries chain algebra chain complex chain functor chain map Coef coefficient functor cohomology commutative diagram coproducts CW-complex cylinder defined Definition element enveloping functor exact sequence example exists fibrant finiteness obstruction free object full subcategory G-space given groupoid GTop hand side Hence homological cofibration category homology homomorphism homotopy category homotopy equivalence homotopy groups homotopy theory I-category inclusion induced map initial object isomorphism Lemma Let f map f map ƒ mod(x mod(x)-module model category module Moreover morphisms obstruction theory obtain pair principal cofibration Proof push out diagram relative CW-complex result Ringoids simplicial groups simplicial objects spaces subcomplex surjective T-complex theory of coactions theory of cogroups topology trivial twisted chain complex twisted homotopy weak equivalence Wh(L Whitehead theorem Xn+1 yields