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On the cube of the equivariant linking pairing

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Niveau: Supérieur, Doctorat, Bac+8
Background Statements The construction On the cube of the equivariant linking pairing for closed 3-manifolds of rank 1 Christine Lescop CNRS, Institut Fourier, Grenoble Chern-Simons Gauge Theory: 20 years after Hausdorff Center for mathematics, Bonn, August 2009 Cube of equivariant linking pairing for M3 with ?1 = 1 Background Statements The construction In this talk, all the manifolds are oriented . A homology sphere is a closed (connected, compact, without boundary) 3–manifold N such that H?(N;Z) = H?(S3;Z). Cube of equivariant linking pairing for M3 with ?1 = 1 Background Statements The construction The study of 3–manifold invariants built from integrals over configuration spaces started after the work of Witten on Chern-Simons theory in 1989, with work of Axelrod, Singer, Kontsevich, Bott, Cattaneo, Taubes... For the knots and links case, many more authors were involved including Bar-Natan, Guadagnini, Martellini, Mintchev, Altschüler, Freidel, Poirier... In 1999, G. Kuperberg and D. Thurston proved that some of these invariants (the Kontsevich ones) fit in with the framework of finite type invariants of homology spheres studied by Ohtsuki, Le, Murakami (2), Goussarov, Habiro, Rozansky, Garoufalidis, Polyak... and together define a universal finite type invariant for homology 3-spheres.

  • dimensional chains

  • rw withw ?


  • rational

  • i∆kx ??

  • kuperberg-thurston work

  • r? s2

  • cyclic covering

  • lemma let


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Language English
Background Statements The construction
On the cube of the equivariant linking pairing for closed3-manifolds of rank1
Christine Lescop
CNRS, Institut Fourier, Grenoble
Chern-Simons Gauge Theory: 20 years after
Hausdorff Center for mathematics, Bonn, August 2009
3 Cube of equivariant linking pairing forMwithβ=1 1
Background Statements The construction The study of3–manifold invariantsbuilt from integrals over configuration spacesstarted after the work of Witten on Chern-Simons theory in 1989, with work of Axelrod, Singer, Kontsevich, Bott, Cattaneo, Taubes... For the knots and links case, many more authors were involved including Bar-Natan, Guadagnini, Martellini, Mintchev, Altschüler, Freidel, Poirier... In 1999, G. Kuperberg and D. Thurston proved that some of these invariants (the Kontsevich ones) fit in with the framework of finite type invariants of homology spheres studied by Ohtsuki, Le, Murakami (2), Goussarov, Habiro, Rozansky, Garoufalidis, Polyak... and together define a universal finite type invariantfor homology3-spheres. 3 Cube of equivariant linking pairing forMwithβ=1 1
Background Statements The construction
In this talk, all the manifolds areoriented .
A homologysphere is a closed (connected, compact, without boundary) 3 3–manifoldNsuch thatH(N;Z) =H(S;Z).
Background Statements The construction
3 Cube of equivariant linking pairing forMwithβ=1 1
In particular, theKuperberg-Thurston workshows how to write Z 1 3 λ(N) =ω Casson, 19842 6 (N\{∞})\diagonal for a homology sphereN,∞ ∈N, and a closed 2-formωsuch that R for any 2-component link(J,L)ofN,ω=lk(J,L). J×L L
11 JL:SSN\ {∞}J 2 11 inducesJ×L:S×S(N\ {∞})\diagonal.
6λ(N)may be viewed as thecube of the linking form. Casson
3 Cube of equivariant linking pairing forMwithβ=1 1