Colloquium Mathematics: Dr. A.V. Kiselev

Join us for coffee and tea at 15.30h

Title: The heptagon-wheel cocycle in the Kontsevich graph complex.

Abstract:

The real vector space of finite non-oriented graphs is known to carry a structure of differential graded Lie algebra (dgLa). We recall that construction and we illustrate it by using the tetrahedral cocycle (Kontsevich 1996) and the Kontsevich—Willwacher pentagon-wheel cocycle, which consists of two graphs with real coefficients. (Under the orientation mapping, either of the two examples yields an infinitesimal symmetry of the spaces of Poisson structures that is universal with respect to all finite-dimensional affine Poisson manifolds.)

The existence of an infinite sequence of nontrivial cocycles in the non-oriented graph complex has been stated by Willwacher: every such cocycle contains a (2m+1)-gon wheel with a nonzero coefficient at some integer m>0 (e.g., see above for m=1 and m=2, respectively).These cocycles generate a noncommutative Lie algebra, the properties of which are largely unexplored. In this talk, the heptagon-wheel cocycle at m=3 will be represented using 46 graphs on 8 vertices and 14 edges (see [1710.00658]).

Colloquium coordinators are Prof.dr. A.J. van der Schaft ( a.j.van.der.schaft rug.nl ),

Dr. A.V. Kiselev (e-mail: a.v.kiselev rug.nl )

http://www.rug.nl/research/jbi/news/colloquia/mathematics-colloquia/