603 research outputs found
Measures on Banach Manifolds, Random Surfaces, and Nonperturbative String Field Theory with Cut-offs
We construct a cut-off version of nonpertubative closed Bosonic string field
theory in the light-cone gauge with imaginary string coupling constant. We show
that the partition function is a continuous function of the string coupling
constant, and conjecture a relation between the formal power series expansion
of this partition function and Riemann Surfaces
The cohomology rings of abelian symplectic quotients
Let be a symplectic manifold, equipped with a Hamiltonian action of a
torus . We give an explicit formula for the rational cohomology ring of the
symplectic quotient in terms of the cohomology ring of and fixed
point data. Under some restrictions, our formulas apply to integral cohomology.
In certain cases these methods enable us to show that the cohomology of the
reduced space is torsion-free
On the cohomology rings of Hamiltonian T-spaces
Let be a symplectic manifold equipped with a Hamiltonian action of a
torus . Let denote the fixed point set of the -action and let
denote the inclusion. By a theorem of F. Kirwan \cite{K}
the induced map in equivariant cohomology is an
injection. We give a simple proof of a formula of Goresky-Kottwitz-MacPherson
\cite{GKM} for the image of the map .Comment: correction to reference
On the growth of solutions to the minimal surface equation over domains containing a halfplane
We consider minimal graphs u(x,y)>0 over unbounded domains D (with u
vanishing on the boundary of D). Assuming D contains a sector properly
containing a halfplane, we obtain estimates on growth and provide examples
illustrating a range of growth.Comment: 11 pages, one figur
Relations in the cohomology ring of the moduli space of flat -connections on a Riemann surface
We consider the moduli space of flat -connections (up to gauge
transformations) on a Riemann surface, with fixed holonomy around a marked
point. There are natural line bundles over this moduli space; we construct
geometric representatives for the Chern classes of these line bundles, and
prove that the ring generated by these Chern classes vanishes below the
dimension of the moduli space, generalising a conjecture of Newstead.Comment: 30 pages, 10 figures. Several corrections and clarifications; final
versio
On semifree symplectic circle actions with isolated fixed points
Let be a symplectic manifold, equipped with a semifree symplectic circle
action with a finite, nonempty fixed point set. We show that the circle action
must be Hamiltonian, and must have the equivariant cohomology and Chern
classes of
Geometry of the intersection ring and vanishing relations in the cohomology of the moduli space of parabolic bundles on a curve
We study the ring generated by the Chern classes of tautological line bundles
on the moduli space of parabolic bundles of arbitrary rank on a Riemann
surface. We show the Poincar\'e duals to these Chern classes have simple
geometric representatives. We use this construction to show that the ring
generated by these Chern classes vanishes below the dimension of the moduli
space, in analogy with the Newstead-Ramanan conjecture for stable bundles.Comment: added reference; to appear in Journal of Differential Geometr
The Weighted Euler-Maclaurin Formula for a simple integral polytope
We give an Euler-Maclaurin formula with remainder for the weighted sum of the
values of a smooth function on the integral points in a simple integral
polytope. Our work generalizes the formula obtained by Karshon, Sternberg and
Weitsman in the ''Euler-Maclaurin with remainder for a simple integral
polytope''.Comment: 11 pages; to appear in the Asian Journal of Mathematic
Euler Maclaurin with remainder for a simple integral polytope
We give an Euler Maclaurin formula with remainder for the sum of the values
of a smooth function on the integral points in a simple integral polytope. This
formula is proved by elementary methods.Comment: 25 pages. Also see our previous paper in Proc. Nat. Acad. Sci. 100
no. 2 (2003), 426-433. Revision: added Euler Maclaurin formulas for symbols
and for polynomial
On geometric quantization of -symplectic manifolds
We study the formal geometric quantization of -symplectic manifolds
equipped with Hamiltonian actions of a torus with nonzero leading modular
weight. The resulting virtual -modules are finite dimensional when is
odd, as in [GMW2]; when is even, these virtual modules are not finite
dimensional, and we compute the asymptotics of the representations for large
weight.Comment: 7 page
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