We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a...

Abstract In the setting of higher-dimensional anisotropic Heisenberg group, we compute fundamental solution for sub-Laplacian, and prove Poincaré $$\beta $$ ? -Logarithmic Sobolev inequalities measures as a function this solution.