Combinatorial Foundation of Homology and Homotopy: Applications to Spaces, Diagrams, Transformation Groups, Compactifications, Differential Algebras, Algebraic Theories, Simplicial Objects, and ResolutionsSpringer Science & Business Media, 27 nov 1998 - 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
V | 3 |
VII | 18 |
VIII | 31 |
IX | 40 |
X | 51 |
XII | 61 |
XIII | 71 |
XV | 87 |
LIII | 225 |
LIV | 229 |
LVI | 231 |
LVII | 234 |
LVIII | 240 |
LIX | 245 |
LX | 249 |
LXII | 254 |
XVI | 89 |
XVII | 95 |
XVIII | 99 |
XX | 101 |
XXI | 110 |
XXII | 115 |
XXIII | 118 |
XXIV | 120 |
XXV | 124 |
XXVI | 127 |
XXVII | 129 |
XXIX | 134 |
XXX | 139 |
XXXI | 145 |
XXXII | 149 |
XXXIII | 156 |
XXXIV | 161 |
XXXV | 169 |
XXXVI | 170 |
XXXVII | 174 |
XXXVIII | 177 |
XXXIX | 182 |
XL | 187 |
XLI | 192 |
XLII | 193 |
XLIII | 197 |
XLIV | 203 |
XLVI | 207 |
XLVII | 209 |
XLVIII | 214 |
XLIX | 215 |
L | 217 |
LI | 221 |
LII | 223 |
LXIII | 257 |
LXIV | 260 |
LXV | 262 |
LXVI | 267 |
LXVIII | 271 |
LXIX | 276 |
LXX | 277 |
LXXI | 279 |
LXXII | 283 |
LXXIII | 286 |
LXXIV | 287 |
LXXV | 291 |
LXXVI | 294 |
LXXVII | 296 |
LXXVIII | 301 |
LXXX | 303 |
LXXXI | 304 |
LXXXII | 312 |
LXXXIII | 315 |
LXXXV | 317 |
LXXXVI | 319 |
LXXXVII | 323 |
LXXXVIII | 327 |
LXXXIX | 328 |
XC | 330 |
XCI | 334 |
XCII | 339 |
XCIII | 342 |
XCIV | 344 |
XCV | 345 |
355 | |
361 | |
Otras ediciones - Ver todo
Combinatorial Foundation of Homology and Homotopy: Applications to Spaces ... Hans-Joachim Baues Vista previa restringida - 2013 |
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 Ho(C homological cofibration category homology homomorphism homotopy category homotopy equivalence homotopy groups homotopy theory inclusion induced map initial object isomorphism Lemma Let f map f map ƒ mod(x model category module Moreover morphisms obstruction theory obtain On+1 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 topological trivial twisted chain complex twisted homotopy weak equivalence Wh(L Whitehead group Whitehead theorem Xn+1 yields