Global surgery formula for the Casson-Walker invariant / / by Christine Lescop

• Autore: Lescop Christine <1966->
• Pubblicazione: Princeton, New Jersey : , : Princeton University Press, , 1996; ©1996
• Descrizione fisica: 1 online resource (156 p.)
• Disciplina: 514/.72
• Soggetto topico: Surgery (Topology); Three-manifolds (Topology)
• Soggetto non controllato: 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
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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 -- Index
• Sommario/riassunto: This 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.
• Titolo autorizzato: Global surgery formula for the Casson-Walker invariant
• ISBN: 0-691-02133-3; 1-4008-6515-8
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910786748103321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; Number 10.