ETH Zurich
Algebra-Topology Seminar,  Oct 15, 2pm.

Title: Polynomial invariants of graphs on surfaces and virtual knots.
	
Abstract:
There is a natural (Euler-Poincare) duality of graphs cellularly  
embedded into a surface. The faces of one graph correspond to vertices 
of its dual and the edges of the graph transversally intersect the 
correspondent edges of the dual graph at a single point. We generalize 
this duality to a duality with respect to a subset of edges. The dual 
graph might be embedded into a different (genus) surface. Moreover 
this generalized duality works for embeddings to non-orientable 
surfaces as well. For graphs on surfaces there is a generalization of 
the Tutte polynomial called the Bollobas-Riordan polynomial. I will 
explain a relation between the Bollobas-Riordan polynomials of dual 
graphs and give an application of it to the knot theory. The results 
are explained in arXiv:0711.3490.