TY - BOOK ID - 1869710 TI - The classifying spaces for surgery and cobordism of manifolds AU - Madsen, Ib Henning AU - Milgram, R. James PY - 1979 SN - 0691082251 069108226X 1400881471 PB - Princeton : Tokyo : Princeton University Press Tokyo university press, DB - UniCat KW - Algebraic topology KW - 515.16 KW - Classifying spaces KW - Cobordism theory KW - Manifolds (Mathematics) KW - Surgery (Topology) KW - Differential topology KW - Homotopy equivalences KW - Topology KW - Geometry, Differential KW - Spaces, Classifying KW - Fiber bundles (Mathematics) KW - Fiber spaces (Mathematics) KW - Topology of manifolds KW - Classifying spaces. KW - Cobordism theory. KW - Manifolds (Mathematics). KW - Surgery (Topology). KW - 515.16 Topology of manifolds KW - Bijection. KW - Calculation. KW - Characteristic class. KW - Classification theorem. KW - Classifying space. KW - Closed manifold. KW - Cobordism. KW - Coefficient. KW - Cohomology. KW - Commutative diagram. KW - Commutative property. KW - Complex projective space. KW - Connected sum. KW - Corollary. KW - Cup product. KW - Diagram (category theory). KW - Differentiable manifold. KW - Disjoint union. KW - Disk (mathematics). KW - Effective method. KW - Eilenberg–Moore spectral sequence. KW - Elaboration. KW - Equivalence class. KW - Exact sequence. KW - Exterior algebra. KW - Fiber bundle. KW - Fibration. KW - Function composition. KW - H-space. KW - Homeomorphism. KW - Homomorphism. KW - Homotopy fiber. KW - Homotopy group. KW - Homotopy. KW - Hopf algebra. KW - Iterative method. KW - Loop space. KW - Manifold. KW - Massey product. KW - N-sphere. KW - Normal bundle. KW - Obstruction theory. KW - Pairing. KW - Permutation. KW - Piecewise linear manifold. KW - Piecewise linear. KW - Polynomial. KW - Prime number. KW - Projective space. KW - Sequence. KW - Simply connected space. KW - Special case. KW - Spin structure. KW - Steenrod algebra. KW - Subset. KW - Summation. KW - Tensor product. KW - Theorem. KW - Topological group. KW - Topological manifold. KW - Topology. KW - Total order. KW - Variétés topologiques KW - Topologie differentielle UR - https://www.unicat.be/uniCat?func=search&query=sysid:1869710 AB - Beginning with a general discussion of bordism, Professors Madsen and Milgram present the homotopy theory of the surgery classifying spaces and the classifying spaces for the various required bundle theories. The next part covers more recent work on the maps between these spaces and the properties of the PL and Top characteristic classes, and includes integrality theorems for topological and PL manifolds. Later chapters treat the integral cohomology of BPL and Btop. The authors conclude with a discussion of the PL and topological cobordism rings and a construction of the torsion-free generators. ER -