scholarly journals Real polarization of the moduli space of flat connections on a Riemann surface

1992 ◽  
Vol 145 (3) ◽  
pp. 425-433 ◽  
Author(s):  
Jonathan Weitsman
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Flat Connections ◽  
Real Polarization

Moduli Space of Flat Connections as a Poisson Manifold

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3195-3206 ◽  
Author(s):  
V. V. Fock ◽  
A. A. Rosly
Keyword(s):  
Riemann Surface ◽  
Lie Groups ◽  
Poisson Structure ◽  
Moduli Space ◽  
Poisson Manifold ◽  
Gauge Fields ◽  
Two Dimensional ◽  
Flat Connections ◽  
Lattice Gauge ◽  
Poisson Lie Groups

In this talk we describe the Poisson structure of the moduli space of flat connections on a two dimensional Riemann surface in terms of lattice gauge fields and Poisson–Lie groups.

Symplectic Geometry of the Moduli Space of Flat Connections on a Riemann Surface: Inductive Decompositions and Vanishing Theorems

2000 ◽  
Vol 52 (3) ◽  
pp. 582-612 ◽  
Author(s):  
Lisa C. Jeffrey ◽  
Jonathan Weitsman
Keyword(s):  
Riemann Surface ◽  
Moduli Space ◽  
Chern Class ◽  
Boundary Component ◽  
Symplectic Geometry ◽  
Line Bundles ◽  
Vanishing Theorems ◽  
Stable Bundles ◽  
Flat Connections ◽  
First Chern Class

AbstractThis paper treats the moduli space g,1(Λ) of representations of the fundamental group of a Riemann surface of genus g with one boundary component which send the loop around the boundary to an element conjugate to exp Λ, where Λ is in the fundamental alcove of a Lie algebra. We construct natural line bundles over g,1(Λ) and exhibit natural homology cycles representing the Poincaré dual of the first Chern class. We use these cycles to prove differential equations satisfied by the symplectic volumes of these spaces. Finally we give a bound on the degree of a nonvanishing element of a particular subring of the cohomology of the moduli space of stable bundles of coprime rank k and degree d.

scholarly journals Half density quantization of the moduli space of flat connections and witten's semiclassical manifold invariants

Topology ◽  
1993 ◽  
Vol 32 (3) ◽  
pp. 509-529 ◽  
Author(s):  
Lisa C. Jeffrey ◽  
Jonathan Weitsman
Keyword(s):  
Moduli Space ◽  
Flat Connections

scholarly journals The Volume of the Moduli Space of Flat Connections on a Nonorientable 2-Manifold

2005 ◽  
Vol 256 (3) ◽  
pp. 539-564 ◽  
Author(s):  
Nan-Kuo Ho ◽  
Lisa C. Jeffrey
Keyword(s):  
Moduli Space ◽  
Flat Connections
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