We study the turbulent velocity dispersion spectra of the coexistent HCN and HCO+ molecular species as a function of length scale in the M17 star-forming molecular cloud. We show that the observed downward shift of the ions spectrum relative to that
of the neutral is readily explained by the existence of an ambipolar diffusion range within which ion and neutral turbulent energies dissipate differently. We use these observations to evaluate this decoupling scale and show how to estimate the strength of the plane-of-the-sky component of the embedded magnetic field in a completely novel way.
We introduce a certain type of representations for the quantum Teichmuller space of a punctured surface, which we call local representations. We show that, up to finitely many choices, these purely algebraic representations are classified by classica
l geometric data. We also investigate the family of intertwining operators associated to such a representations. In particular, we use these intertwiners to construct a natural fiber bundle over the Teichmuller space and its quotient under the action of the mapping class group. This construction also offers a convenient framework to exhibit invariants of surface diffeomorphisms.
