Boundedly controlled topology. Foundations of algebraic topology and simple homotopy theory

zbMath0646.57001MaRDI QIDQ1210752

Douglas R. Anderson, Hans Jørgen Munkholm

Publication date: 5 June 1993

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

zbMATH Keywords

Whitehead groupsK-theoryhomology invariantsfundamental groupoidStiefel-Whitney classeshomotopy groupsHurewicz theoremsWhitehead torsioncategories of fractionssimple homotopy theoryboundedly controlled topologyalgebraic Whitehead groupbc CW complexbc PL h-cobordismboundedly controlled spaceboundedness control structurecategory with endomorphismcellular approximation theoremfragmented spaces- cobordism theorem

Mathematics Subject Classification ID

Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. (57Q10) (h)- and (s)-cobordism (57R80) Topological (K)-theory (55N15) Other homology theories in algebraic topology (55N35) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Categorical structures (18D99) Functor categories, comma categories (18A25) Groupoids, semigroupoids, semigroups, groups (viewed as categories) (18B40) Homotopy groups of special types (55Q70)

Related Items (7)

Bounded Surgery and Dihedral Group Actions on Spheres ⋮ A comparison of continuously controlled and controlled \(K\)-theory ⋮ Boundedly controlled algebraic \(K\)-theory of spaces and its linear counterexamples ⋮ The \(K\)-theoretic Farrell-Jones conjecture for hyperbolic groups ⋮ Monoidal controlled Poincaré duality ⋮ The Boundedly Controlled Whitehead Theorem ⋮ The Bounded and Thin Whitehead Theorems

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