On homeomorphisms and quasi-isometries of the real line

We show that the group of all pl-homeomorphisms of the reals having bounded slopes surjects on the group $QI({\Bbb R})$ of all quasi-isometries of ${\Bbb R}$. We prove that the following groups can be imbedded in $QI({\Bbb R})$: The group of compactly supported pl-homeomorphisms of the reals, the Richard Thompson group F, and the free group of rank the continuum.Comment: 9 page

K theory of smooth complete toric varieties and related spaces

The K-rings of non-singular complex pro jective varieties as well as quasi- toric manifolds were described in terms of generators and relations in an earlier work of the author with V. Uma. In this paper we obtain a similar description for complete non-singular toric varieties. Indeed, our approach enables us to obtain such a description for the more general class of torus manifolds with locally standard torus action and orbit space a homology polytope.Comment: 11 pages, no figure

A model of the diffuse galactic gamma ray emission

The galaxy was observed to be a source of high energy gamma rays as shown by the two successful satellite experiments, SAS-2 and COS-B. It is generally understood that these diffuse gamma rays result from interactions between energetic cosmic rays and interstellar gas. This work makes use of the most recent data on the distribution of atomic and molecular hydrogen in the galaxy along with new estimates of gamma ray production functions to model the diffuse galactic gamma ray emission. The model allows various spatial distributions for cosmic rays in the Galaxy including non-axisymmetric ones. In the light of the expected data from EGRET (Energetic Gamma-Ray Experiment Telescope), an improved model of cosmic ray-matter-gamma ray interaction will provide new insights into the distribution of cosmic rays and the strength of its coupling to matter

Vector Fields on certain quotients of complex Stiefel manifolds

We consider quotients of complex Stiefel manifolds by finite cyclic groups whose action is induced by the scalar multiplication on the corresponding complex vector space. We obtain a description of their tangent bundles, compute their mod p cohomology and obtain estimates for their span (with respect to their standard differentiable structure). We compute the Pontrjagin and Stiefel-Whitney classes of these manifolds and give applications to their stable parallelizability

Open String Diagrams I: Topological Type

An arbitrary Feynman graph for string field theory interactions is analysed and the homeomorphism type of the corresponding world sheet surface is completely determined even in the non-orientable cases. Algorithms are found to mechanically compute the topological characteristics of the resulting surface from the structure of the signed oriented graph. Whitney's permutation-theoretic coding of graphs is utilized

An analogue of the Narasimhan-Seshadri theorem and some applications

We prove an analogue in higher dimensions of the classical Narasimhan-Seshadri theorem for strongly stable vector bundles of degree 0 on a smooth projective variety $X$ with a fixed ample line bundle $\Theta$. As applications, over fields of characteristic zero, we give a new proof of the main theorem in a recent paper of Balaji and Koll\'ar and derive an effective version of this theorem; over uncountable fields of positive characteristics, if $G$ is a simple and simply connected algebraic group and the characteristic of the field is bigger than the Coxeter index of $G$, we prove the existence of strongly stable principal $G$ bundles on smooth projective surfaces whose holonomy group is the whole of $G$.Comment: 42 pages. Theorem 3 of this version is new. Typos have been corrected. To appear in Journal of Topolog

Spin-catalyzed hopping conductivity in disordered strongly interacting quantum wires

In one-dimensional electronic systems with strong repulsive interactions, charge excitations propagate much faster than spin excitations. Such systems therefore have an intermediate temperature range [termed the "spin-incoherent Luttinger liquid'" (SILL) regime] where charge excitations are "cold" (i.e., have low entropy) whereas spin excitations are "hot." We explore the effects of charge-sector disorder in the SILL regime in the absence of external sources of equilibration. We argue that the disorder localizes all charge-sector excitations; however, spin excitations are protected against full localization, and act as a heat bath facilitating charge and energy transport on asymptotically long timescales. The charge, spin, and energy conductivities are widely separated from one another. The dominant carriers of energy are neither charge nor spin excitations, but neutral "phonon" modes, which undergo an unconventional form of hopping transport that we discuss. We comment on the applicability of these ideas to experiments and numerical simulations.Comment: 14 pages, 6 figure