Topological Methods in Group TheorySpringer Science & Business Media, 17.12.2007 - 473 Seiten This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit. |
Inhalt
Contents | 2 |
Cellular Homology | 35 |
Fundamental Group and Tietze Transformations | 73 |
Some Techniques in Homotopy Theory | 101 |
Elementary Geometric Topology | 125 |
FINITENESS PROPERTIES OF GROUPS | 141 |
Topological Finiteness Properties and Dimension of Groups | 161 |
KG 1 complexes | 169 |
5 | 214 |
Cohomology of CW Complexes | 259 |
TOPICS IN THE COHOMOLOGY OF INFINITE | 283 |
Filtered Ends of Pairs of Groups | 333 |
Poincaré Duality in Manifolds and Groups 353 | 352 |
HOMOTOPICAL GROUP THEORY | 367 |
Higher homotopy theory of groups | 411 |
THREE ESSAYS 431 | 430 |
3 | 176 |
2 | 185 |
Finiteness Properties of Some Important Groups | 197 |
4 | 203 |
References | 453 |
| 462 | |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
abelian algebraic base point bijection cell cellular map chain complex characteristic map cohomology commutative diagram compact Corollary countable covering projection covering space CW complex CW complex structure CW-proper defined deformation retract denoted edge loop edge path example exercise filtration finite CW complex finite index finitely presented fundamental group G has type G-CW group G Hausdorff hence homeomorphism homology homotopy equivalence induces infinite inverse limit inverse sequence isomorphism Lemma Let f Let G locally finite locally finite type manifold map f map ƒ metric modules monomorphism morphism n-cells n-connected n-manifold n-skeleton path component Proof proper homotopy proper ray properties Proposition Prove quasi-isometry quotient map R-module resp Sect semistable short exact sequence simplex simplicial complex simply connected strong deformation retract subcomplex subgroup Theorem theory topology trivial type F universal cover vertex vertices α α
