LEADER 05003nam 2200685Ia 450 001 9910455594703321 005 20200520144314.0 010 $a1-282-76067-X 010 $a9786612760679 010 $a981-283-687-X 035 $a(CKB)2490000000001691 035 $a(EBL)1679564 035 $a(OCoLC)729020484 035 $a(SSID)ssj0000948772 035 $a(PQKBManifestationID)11563832 035 $a(PQKBTitleCode)TC0000948772 035 $a(PQKBWorkID)10951552 035 $a(PQKB)10196450 035 $a(MiAaPQ)EBC1679564 035 $a(Au-PeEL)EBL1679564 035 $a(CaPaEBR)ebr10422058 035 $a(CaONFJC)MIL276067 035 $a(EXLCZ)992490000000001691 100 $a20101028d2010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aTopological library$hPart 2$iCharacteristic classes and smooth structures on manifolds$b[electronic resource] /$feditors, S.P. Novikov, I.A. Taimanov ; translated by V.O. Manturov 210 $aHackensack, N.J. $cWorld Scientific$dc2010 215 $a1 online resource (278 p.) 225 1 $aSeries on knots and everything ;$vv. 44 300 $aOriginally published in Russian. 311 $a981-283-686-1 320 $aIncludes bibliographical references. 327 $aContents; S. P. Novikov's Preface; 1 J. Milnor. On manifolds homeomorphic to the 7-sphere; 1. The invariant ?(M7); 2. A partial characterization of the n-sphere; 3. Examples of 7-manifolds; 4. Miscellaneous results; References; 2 M. Kervaire and J. Milnor. Groups of homotopy spheres. I; 1. Introduction; 2. Construction of the group ?n; 3. Homotopy spheres are s-parallelizable; 4. Which homotopy spheres bound parallelizable manifolds?; 5. Spherical modifications; 6. Framed sphericalmodifications; 7. The groups bP2k; 8. A cohomology operation; References 327 $a3 S. P. Novikov. Homotopically equivalent smooth manifoldsIntroduction; Chapter I. The fundamental construction; 1. Morse's surgery; 2. Relative ?-manifolds; 3. The general construction; 4. Realization of classes; 5. The manifolds in one class; 6. Onemanifold in different classes; Chapter II. Processing the results; 7. The Thom space of a normal bundle. Its homotopy structure; 8. Obstructions to a di.eomorphism of manifolds having the same homotopy type and a stable normal bundle; 9. Variation of a smooth structure keeping triangulation preserved 327 $a 10. Varying smooth structure and keeping the triangulation preserved.Morse surgeryChapter III. Corollaries and applications; 11. Smooth structures on Cartesian product of spheres; 12. Low-dimensional manifolds. Cases n = 4, 5, 6, 7; 13. Connected sum of a manifold with Milnor's sphere; 14. Normal bundles of smooth manifolds; Appendix 1. Homotopy type and Pontrjagin classes; Appendix 2. Combinatorial equivalence and Milnor's microbundle theory; Appendix 3. On groups ; Appendix 4. Embedding of homotopy spheres into Euclidean space and the suspension stable homomorphism 327 $aIntroduction 1. Formulation of results; 2. The proof scheme of main theorems; 3. A geometrical lemma; 4. An analog of the Hurewicz theorem; 5. The functor P = Homc and its application to the study of homology properties of degree one maps; 6. Stably freeness of kernel modules under the assumptions of Theorem 3; 7. The homology effect of a Morse surgery; 8. Proof of Theorem 3; 9. Proof of Theorem 6; 10. One generalization of Theorem 5; Appendix 1. On the signature formula; Appendix 2. Unsolved questions concerning characteristic class theory 327 $aAppendix 3. Algebraic remarks about the functor P = Homc 330 $a This is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s-1960s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated "singular homologies of fiber spaces." Sample Chapter(s)
Chapter 1: On manifolds homeomorphic to the 7-sphere1 (153 KB)

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