Differential operators and flat connections on a Riemann surface
نویسندگان
چکیده
منابع مشابه
Differential Operators and Flat Connections on a Riemann Surface
We consider filtered holomorphic vector bundles on a compact Riemann surface X equipped with a holomorphic connection satisfying a certain transversality condition with respect to the filtration. If Q is a stable vector bundle of rank r and degree (1−genus(X))nr , then any holomorphic connection on the jet bundle Jn(Q) satisfies this transversality condition for the natural filtration of Jn(Q) ...
متن کاملExterior differential algebras and flat connections on Weyl groups
We study some aspects of noncommutative differential geometry on a finite Weyl group in the sense of S. Woronowicz, K. Bresser et al., and S. Majid. For any finite Weyl group W we consider the subalgebra generated by flat connections in the left-invariant exterior differential algebra of W. For root systems of type A and D we describe a set of relations between the flat connections, which conje...
متن کاملPoisson structure on moduli of flat connections on Riemann surfaces and r - matrix
We consider the space of graph connections (lattice gauge fields) which can be endowed with a Poisson structure in terms of a ciliated fat graph. (A ciliated fat graph is a graph with a fixed linear order of ends of edges at each vertex.) Our aim is however to study the Poisson structure on the moduli space of locally flat vector bundles on a Riemann surface with holes (i.e. with boundary). It ...
متن کاملFlat connections, geometric invariants and energy of harmonic functions on compact Riemann surfaces
This work grew out of an attempt to generalize the construction of Chern-Simons invariants. In this paper, we associate a geometric invariant to the space of flat connection on a SU(2)-bundle on a compact Riemann surface and relate it to the energy of harmonic functions on the surface. Our set up is as follows. Let G = SU(2) and M be a compact Riemann surface and E ~ M be the trivial G-bundle. ...
متن کاملA Riemann–roch–hirzebruch Formula for Traces of Differential Operators
Let D be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an n-dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, giving the Lefschetz number of D as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2003
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171203212187