Leseprobe
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Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140
Christine Lescop
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Homotopy sphere, Tubular neighborhood, Change of basis, Taylor series, Polynomial, Topology, Casson invariant, Permutation, Ambient isotopy, Projective plane, Symmetrization, Alexander polynomial, Prime number, Connected component (graph theory), Fiber bundle, Fundamental group, Addition, Computation, Unlink, Combinatorics, Function (mathematics), Integer, Indeterminate (variable), Disk (mathematics), Homology sphere, Connected sum, Cobordism, Notation, Combination, Conjugacy class, Change of variables, Fibration, Scientific notation, Connected space, Theorem, 3-manifold, Empty set, Morphism, Sequence, Cup product, Homeomorphism, Betti number, Determinant, Manifold, Coefficient, Knot theory, Homology (mathematics), Seifert surface, Exterior (topology), Summation, Orientability, Klein bottle, Diagram (category theory)