03503nam 22005655 450 991025545570332120200701155046.03-319-71306-X10.1007/978-3-319-71306-9(CKB)4100000001794754(DE-He213)978-3-319-71306-9(MiAaPQ)EBC5247432(PPN)223955612(EXLCZ)99410000000179475420180125d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierThe Geometric Hopf Invariant and Surgery Theory /by Michael Crabb, Andrew Ranicki1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (XVI, 397 p. 1 illus. in color.) Springer Monographs in Mathematics,1439-73823-319-71305-1 Includes bibliographical references and index.1 The difference construction -- 2 Umkehr maps and inner product spaces -- 3 Stable homotopy theory -- 4 Z_2-equivariant homotopy and bordism theory -- 5 The geometric Hopf invariant -- 6 The double point theorem -- 7 The -equivariant geometric Hopf invariant -- 8 Surgery obstruction theory -- A The homotopy Umkehr map -- B Notes on Z2-bordism -- C The geometric Hopf invariant and double points (2010) -- References -- Index.Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. .Springer Monographs in Mathematics,1439-7382Algebraic topologyManifolds (Mathematics)Complex manifoldsAlgebraic Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28019Manifolds and Cell Complexes (incl. Diff.Topology)https://scigraph.springernature.com/ontologies/product-market-codes/M28027Algebraic topology.Manifolds (Mathematics).Complex manifolds.Algebraic Topology.Manifolds and Cell Complexes (incl. Diff.Topology).514.24Crabb Michaelauthttp://id.loc.gov/vocabulary/relators/aut767648Ranicki Andrewauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910255455703321The Geometric Hopf Invariant and Surgery Theory2044176UNINA