The classifying spaces for surgery and cobordism of manifolds. (English) Zbl 0446.57002

Madsen, Ib; Milgram, R. James

Annals of Mathematics Studies, 92. Princeton, New Jersey: Princeton University Press; University of Tokyo Press. XII, 280 p. $ 20.00 (1979).

MSC:

57-02	Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes
57N70	Cobordism and concordance in topological manifolds
57Q20	Cobordism in PL-topology
57R65	Surgery and handlebodies
57T25	Homology and cohomology of \(H\)-spaces
57T35	Applications of Eilenberg-Moore spectral sequences
57R67	Surgery obstructions, Wall groups
57Q60	Cobordism and concordance in PL-topology
55-02	Research exposition (monographs, survey articles) pertaining to algebraic topology
55P47	Infinite loop spaces
55R25	Sphere bundles and vector bundles in algebraic topology
55R35	Classifying spaces of groups and \(H\)-spaces in algebraic topology
55R40	Homology of classifying spaces and characteristic classes in algebraic topology
55R50	Stable classes of vector space bundles in algebraic topology and relations to \(K\)-theory
55T20	Eilenberg-Moore spectral sequences
55T99	Spectral sequences in algebraic topology

Keywords:

bordism rings of piecewise linear and topological manifolds; classifying space for topological sphere bundles away from 2; characteristic classes; cobordism; simply connected surgery; mod 2 spherical characteristic classes; infinite loop space theory; G/TOP; delooping; cohomology of BPL and BTOP; PL genus; integrality; Bockstein spectral sequence; relations involving Milnor manifolds