Non-orientable quasi-trees for the Bollobas-Riordan polynomial

Abstract

We extend the quasi-tree expansion of A. Champanerkar, I. Kofman, and N. Stoltzfus to not necessarily orientable ribbon graphs. We study the duality properties of the Bollobas-Riordan polynomial in terms of this expansion. As a corollary, we get a "connected state" expansion of the Kauffman bracket of virtual link diagrams. Our proofs use extensively the partial duality of S. Chmutov.