05272nam 2201309 450 991078674810332120230421031020.00-691-02133-31-4008-6515-810.1515/9781400865154(CKB)3710000000222319(EBL)1756193(OCoLC)888743940(SSID)ssj0001332954(PQKBManifestationID)12539094(PQKBTitleCode)TC0001332954(PQKBWorkID)11396104(PQKB)10042620(MiAaPQ)EBC1756193(DE-B1597)447742(OCoLC)887802708(OCoLC)979780764(DE-B1597)9781400865154(Au-PeEL)EBL1756193(CaPaEBR)ebr10909209(CaONFJC)MIL637571(OCoLC)891398210(EXLCZ)99371000000022231920140830h19961996 uy 0engur|nu---|u||utxtccrGlobal surgery formula for the Casson-Walker invariant /by Christine LescopPrinceton, New Jersey :Princeton University Press,1996.©19961 online resource (156 p.)Annals of Mathematics Studies ;Number 10Description based upon print version of record.1-322-06320-6 0-691-02132-5 Includes bibliographical references and index.Front matter --Table of contents --Chapter 1. Introduction and statements of the results --Chapter 2. The Alexander series of a link in a rational homology sphere and some of its properties --Chapter 3. Invariance of the surgery formula under a twist homeomorphism --Chapter 4. The formula for surgeries starting from rational homology spheres --Chapter 5. The invariant A. for 3-manifolds with nonzero rank --Chapter 6. Applications and variants of the surgery formula --Appendix. More about the Alexander series --Bibliography --IndexThis book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S 3. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S 3 is described, and it is proven that F consistently defines an invariant, lamda (l), of closed oriented 3-manifolds. l is then expressed in terms of previously known invariants of 3-manifolds. For integral homology spheres, l is the invariant introduced by Casson in 1985, which allowed him to solve old and famous questions in 3-dimensional topology. l becomes simpler as the first Betti number increases. As an explicit function of Alexander polynomials and surgery coefficients of framed links, the function F extends in a natural way to framed links in rational homology spheres. It is proven that F describes the variation of l under any surgery starting from a rational homology sphere. Thus F yields a global surgery formula for the Casson invariant.Annals of mathematics studies ;Number 10.Surgery (Topology)Three-manifolds (Topology)3-manifold.Addition.Alexander polynomial.Ambient isotopy.Betti number.Casson invariant.Change of basis.Change of variables.Cobordism.Coefficient.Combination.Combinatorics.Computation.Conjugacy class.Connected component (graph theory).Connected space.Connected sum.Cup product.Determinant.Diagram (category theory).Disk (mathematics).Empty set.Exterior (topology).Fiber bundle.Fibration.Function (mathematics).Fundamental group.Homeomorphism.Homology (mathematics).Homology sphere.Homotopy sphere.Indeterminate (variable).Integer.Klein bottle.Knot theory.Manifold.Morphism.Notation.Orientability.Permutation.Polynomial.Prime number.Projective plane.Scientific notation.Seifert surface.Sequence.Summation.Symmetrization.Taylor series.Theorem.Topology.Tubular neighborhood.Unlink.Surgery (Topology)Three-manifolds (Topology)514/.72Lescop Christine1966-61272MiAaPQMiAaPQMiAaPQBOOK9910786748103321Global surgery formula for the Casson-Walker invariant375767UNINA