Claudio Meneses

Geometry of C-flat connections, coarse graining and the continuum limit

A notion of effective gauge fields which does not involve a background metric is introduced. The role of scale is played by cellular decompositions of the base manifold. Once a cellular decomposition is chosen, the corresponding space of effective gauge fields is the space of flat connections with singularities on its codimension two skeleton, AC‐flat∕G¯M,⋆⊂A¯M∕G¯M,⋆. If cellular decomposition C2 is finer than cellular decomposition C1, there is a coarse graining map πC2→C1:AC2‐flat∕G¯M,⋆→AC1‐flat∕G¯M,⋆. We prove that the triple (AC2‐flat∕G¯M,⋆,πC2→C1,AC1‐flat∕G¯M,⋆) is a principal fiber bundle with a preferred global section given by the natural inclusion map iC1→C2:AC1‐flat∕G¯M,⋆→AC2‐flat∕G¯M,⋆. Since the spaces AC‐flat∕G¯M,⋆ are partially ordered (by inclusion) and this order is directed in the direction of refinement, we can define a continuum limit, C→M. We prove that, in an appropriate sense, limC→MAC‐flat∕G¯M,⋆=A¯M∕G¯M,⋆. We also define a construction of measures in A¯M∕G¯M,⋆ as the continuum limit...

On vector-valued Poincaré series of weight 2

Abstract Given a pair ( Γ , ρ ) of a Fuchsian group of the first kind, and a unitary representation ρ of Γ of arbitrary rank, the problem of construction of vector-valued Poincare series of weight 2 is considered. Implications in the theory of parabolic bundles are discussed. When the genus of the group is zero, it is shown how an explicit basis for the space of these functions can be constructed.

Remarks on groups of bundle automorphisms over the Riemann sphere

A geometric characterization of the structure of the group of automorphisms of an arbitrary Birkhoff–Grothendieck bundle splitting

Singular connections, WZNW action, and moduli of parabolic bundles on the sphere

\oplus _{i=1}^{r} \mathcal {O}(m_{i})

Optimum weight chamber examples of moduli spaces of stable parabolic bundles in genus 0.

⊕i=1rO(mi) over

On a functional of Kobayashi for Higgs bundles

\mathbb {C}\mathbb {P}^{1}