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020 _a9783031563348
_9978-3-031-56334-8
024 7 _a10.1007/978-3-031-56334-8
_2doi
050 4 _aQA613-613.8
072 7 _aPBP
_2bicssc
072 7 _aMAT038000
_2bisacsh
072 7 _aPBP
_2thema
100 1 _aLück, Wolfgang.
_eauthor.
_0(orcid)0000-0003-1141-1422
_1https://orcid.org/0000-0003-1141-1422
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_980072
245 1 0 _aSurgery Theory
_h[electronic resource] :
_bFoundations /
_cby Wolfgang Lück, Tibor Macko.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXV, 956 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x2196-9701 ;
_v362
505 0 _a1 Introduction -- 2 The s-Cobordism Theorem -- 3 Whitehead Torsion -- 4 The Surgery Step and ξ-Bordism -- 5 Poincaré Duality -- 6 The Spivak Normal Structure -- 7 Normal Maps and the Surgery Problem -- 8 The Even-Dimensional Surgery Obstruction -- 9 The Odd-Dimensional Surgery Obstruction -- 10 Decorations and the Simple Surgery Obstruction -- 11 The Geometric Surgery Exact Sequence -- 12 Homotopy Spheres -- 13 The Geometric Surgery Obstruction Group and Surgery Obstruction -- 14 Chain Complexes -- 15 Algebraic Surgery -- 16 Brief Survey of Computations of L-Groups -- 17 The Homotopy Type of G/TOP, G/PL, and G/O -- 18 Computations of Topological Structure Sets of some Prominent Closed Manifolds -- 19 Topological Rigidity -- 20 Modified Surgery -- 21 Solutions of the Exercises.
520 _aThis monograph provides a comprehensive introduction to surgery theory, the main tool in the classification of manifolds. Surgery theory was developed to carry out the so-called Surgery Program, a basic strategy to decide whether two closed manifolds are homeomorphic or diffeomorphic. This book provides a detailed explanation of all the ingredients necessary for carrying out the surgery program, as well as an in-depth discussion of the obstructions that arise. The components include the surgery step, the surgery obstruction groups, surgery obstructions, and the surgery exact sequence. This machinery is applied to homotopy spheres, the classification of certain fake spaces, and topological rigidity. The book also offers a detailed description of Ranicki's chain complex version, complete with a proof of its equivalence to the classical approach developed by Browder, Novikov, Sullivan, and Wall. This book has been written for learning surgery theory and includes numerous exercises. With full proofs and detailed explanations, it also provides an invaluable reference for working mathematicians. Each chapter has been designed to be largely self-contained and includes a guide to help readers navigate the material, making the book highly suitable for lecture courses, seminars, and reading courses.
650 0 _aManifolds (Mathematics).
_969683
650 1 4 _aManifolds and Cell Complexes.
_973090
700 1 _aMacko, Tibor.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_980073
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031563331
776 0 8 _iPrinted edition:
_z9783031563355
830 0 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x2196-9701 ;
_v362
_980074
856 4 0 _uhttps://doi.org/10.1007/978-3-031-56334-8
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c61363
_d61363