Buongiorno a tutti,
vi ricordo del seminario di mercoledì prossimo 6 maggio, alle
16 in sala seminari. Trovate i dati qui sotto.
P Lisca
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Speaker: Ana Garcia Lecuona, Université d'Aix-Marseille.
Titolo: Splice links and colored signatures
Abstract:
The splice of two links is an operation defined by Eisenbund and Neumann
which generalizes several other operations on links, such as the connected
sum, the cabling or the disjoint union. The precise definition will be
given in the talk but the rough idea goes as follows: the splice of the
links L’ and L'' along the components K' and K'' is the link (L' \ K') U
(L''\ K'') obtained by identifying the exterior of K' with the exterior of
K''. There has been much interest to understand the behavior of different
link invariants under the splice operation (genus, fiberability, Conway
polynomial, Heegaard-Floer homology among others) and the goal of this talk
is to present a formula relating the colored signature of the splice of two
oriented links to the colored signatures of its two constituent links. As
an immediate consequence, we have that the conventional univariate
Levine-Tristram signature of a splice depends, in general, on the colored
(or multivariate) signatures of the summands. There is one case for which
we do not have yet a closed formula. If time permits, we will discuss this
case whose study leads to a generalization of Kojima's eta-function for
links.This is a joint work, still in progress, with Alex Degtyarev and
Vincent Florens.