Monopoles and clusters

We define and study certain hyperkaehler manifolds which capture the asymptotic behaviour of the SU(2)-monopole metric in regions where monopoles break down into monopoles of lower charges. The rate at which these new metrics approximate the monopole metric is exponential, as for the Gibbons-Manton metric.Comment: v2.: relation to calorons mentioned; added explanation

A note on monopole moduli spaces

We discuss the structure of the framed moduli space of Bogomolny monopoles for arbitrary symmetry breaking and extend the definition of its stratification to the case of arbitrary compact Lie groups. We show that each stratum is a union of submanifolds for which we conjecture that the natural $L^2$ metric is hyperKahler. The dimensions of the strata and of these submanifolds are calculated, and it is found that for the latter, the dimension is always a multiple of four.Comment: 17 pages, LaTe

Calorons, Nahm's equations on S^1 and bundles over P^1xP^1

The moduli space of solutions to Nahm's equations of rank (k,k+j) on the circle, and hence, of SU(2) calorons of charge (k,j), is shown to be equivalent to the moduli of holomorphic rank 2 bundles on P^1xP^1 trivialized at infinity with c_2=k and equipped with a flag of degree j along P^1x{0}. An explicit matrix description of these spaces is given by a monad constructio

Liouville Integrability of Classical Calogero-Moser Models

Liouville integrability of classical Calogero-Moser models is proved for models based on any root systems, including the non-crystallographic ones. It applies to all types of elliptic potentials, i.e. untwisted and twisted together with their degenerations (hyperbolic, trigonometric and rational), except for the rational potential models confined by a harmonic force.Comment: 8 pages, LaTeX2e, no figure

The Chemorepellent, Netrin-1, Appears to Signal Through a Tyrosine Kinase in Tetrahymena thermophila

Netrin-1 is a pleiotropic peptide signaling molecule. Its most well-known role in vertebrate development is neuronal guidance. Depending upon the cell type and signal concentration gradient, netrin-1 may serve either as a chemoattractant, causing formation of axonal growth cones, or as a chemorepellent, causing growth cone collapse within the axon. Netrin-1 can bind to at least two types of receptors, and uses a variety of signaling proteins to convey its message. In some vertebrate cell types, the netrin-1 signal is G-protein mediated, while in other cell types, netrin signaling requires a tyrosine kinase or some other combination of kinases in order to signal. Tetrahymena thermophila are free-living, eukaryotic cells that can respond to chemoattractants and chemorepellents by moving toward attractants and away from repellents. By studying the behavior of these organisms, we have found that netrin-1 acts as a chemorepellent in T. thermophila. Response to netrin-1 is concentration dependent, with an EC100 of approximately 1 micromolar, and an EC50 of approximately 10 pM. Netrin-1 avoidance may be effectively eliminated by the addition of the broad-spectrum tyrosine kinase inhibitor, genistein, to the behavioral assay. The IC100 of genistein was approximately 75 micrograms/ml, while the IC50 of this compound was near 50 micrograms/ml. G-protein inhibitors, calcium chelators, and a number of other pharmacological inhibitors had no effect on netrin-1 signaling in this organism. These data show that netrin-1 is a chemorepellent in Tetrahymena thermophila and that netrin signaling appears to implicate a tyrosine kinase in this organism. Further studies will help us to determine whether genistein is specifically acting upon a tyrosine kinase pathway or whether the inhibition is occurring via some other genistein-mediated effect

Inversion symmetric 3-monopoles and the Atiyah-Hitchin manifold

We consider 3-monopoles symmetric under inversion symmetry. We show that the moduli space of these monopoles is an Atiyah-Hitchin submanifold of the 3-monopole moduli space. This allows what is known about 2-monopole dynamics to be translated into results about the dynamics of 3-monopoles. Using a numerical ADHMN construction we compute the monopole energy density at various points on two interesting geodesics. The first is a geodesic over the two-dimensional rounded cone submanifold corresponding to right angle scattering and the second is a closed geodesic for three orbiting monopoles.Comment: latex, 22 pages, 2 figures. To appear in Nonlinearit