03547nam 22008295 450 991015474460332120190708092533.01-4008-8246-X10.1515/9781400882465(CKB)3710000000631345(MiAaPQ)EBC4738731(DE-B1597)467922(OCoLC)979743249(DE-B1597)9781400882465(EXLCZ)99371000000063134520190708d2016 fg engurcnu||||||||rdacontentrdamediardacarrierAn Extension of Casson's Invariant. (AM-126), Volume 126 /Kevin WalkerPrinceton, NJ : Princeton University Press, [2016]©19921 online resource (140 pages) illustrationsAnnals of Mathematics Studies ;3080-691-08766-0 0-691-02532-0 Includes bibliographical references.Frontmatter -- Contents -- 0. Introduction -- 1. Topology of Representation Spaces -- 2. Definition of λ -- 3. Various Properties of λ -- 4. The Dehn Surgery Formula -- 5. Combinatorial Definition of λ -- 6. Consequences of the Dehn Surgery Formula -- A. Dedekind Sums -- B. Alexander Polynomials -- BibliographyThis book describes an invariant, l, of oriented rational homology 3-spheres which is a generalization of work of Andrew Casson in the integer homology sphere case. Let R(X) denote the space of conjugacy classes of representations of p(X) into SU(2). Let (W,W,F) be a Heegaard splitting of a rational homology sphere M. Then l(M) is declared to be an appropriately defined intersection number of R(W) and R(W) inside R(F). The definition of this intersection number is a delicate task, as the spaces involved have singularities. A formula describing how l transforms under Dehn surgery is proved. The formula involves Alexander polynomials and Dedekind sums, and can be used to give a rather elementary proof of the existence of l. It is also shown that when M is a Z-homology sphere, l(M) determines the Rochlin invariant of M.Annals of mathematics studies ;no. 126.Three-manifolds (Topology)InvariantsAbsolute value.Andrew Casson.Basis (linear algebra).Cohomology.Dan Freed.Dehn surgery.Dehn twist.Determinant.Diagram (category theory).Disk (mathematics).Elementary proof.Fundamental group.General position.Heegaard splitting.Homology sphere.Identity matrix.Inner product space.Lie group.Mathematical sciences.Morris Hirsch.Normal bundle.Scientific notation.Sequence.Surjective function.Symplectic geometry.Theorem.Topology.Three-manifolds (Topology)Invariants.514/.3SK 320rvkWalker Kevin, 350732DE-B1597DE-B1597BOOK9910154744603321An Extension of Casson's Invariant. (AM-126), Volume 1262786236UNINA