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On a cube of the equivariant link pairingGeometry/Topology
|Speaker:||Christine Lescop, Institut Fourier|
|Start time:||Tue, Oct 15 2013, 4:10PM|
We will describe an invariant of knots in rational homology $3$-spheres and some of its properties. Our invariant is an equivariant algebraic intersection of three representatives of the knot Blanchfield pairing in an equivariant configuration space of pairs of points of the ambient manifold.
We will also briefly outline generalizations of this ``cubic'' topological construction. Our generalizations produce an invariant that is conjecturally equivalent to the Kricker lift of the Kontsevich integral (generalized by Le, Murakami and Ohtsuki) and is indeed equivalent to this lift for knots with trivial Alexander polynomial.