scholarly journals Moduli Spaces of Flat Connections on 2-Manifolds, Cobordism, and Witten’s Volume Formulas

1999 ◽  
pp. 271-295 ◽  
Author(s):  
E. Meinrenken ◽  
C. Woodward
Keyword(s):  
Moduli Spaces ◽  
Flat Connections

scholarly journals On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces

2004 ◽  
Vol 56 (6) ◽  
pp. 1228-1236 ◽  
Author(s):  
Nan-Kuo Ho ◽  
Chiu-Chu Melissa Liu
Keyword(s):  
Lie Groups ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Orientable Surface ◽  
Equivalence Classes ◽  
Nonorientable Surface ◽  
Flat Connections ◽  
Gauge Equivalence ◽  
Compact Orientable Surface ◽  
Simply Connected

AbstractWe study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the compact, connected, simply connected Lie groups, and some non-semisimple classical groups.

scholarly journals GEOMETRY OF MODULI SPACES OF FLAT BUNDLES ON PUNCTURED SURFACES

1998 ◽  
Vol 09 (01) ◽  
pp. 63-73 ◽  
Author(s):  
PHILIP A. FOTH
Keyword(s):  
Riemann Surface ◽  
Conjugacy Class ◽  
Moduli Spaces ◽  
Flat Connections ◽  
Rational Singularities ◽  
Take All

For a Riemann surface with one puncture we consider moduli spaces of flat connections such that the monodromy transformation around the puncture belongs to a given conjugacy class with the property that a product of its distinct eigenvalues is not equal to 1 unless we take all of them. We prove that these moduli spaces are smooth and their natural closures are normal with rational singularities.

scholarly journals Superintegrable Systems on Moduli Spaces of Flat Connections

2021 ◽  
Author(s):  
S. Arthamonov ◽  
N. Reshetikhin
Keyword(s):  
Hamiltonian Systems ◽  
Poisson Structure ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Flat Connections ◽  
Superintegrable Systems ◽  
Poisson Variety

AbstractThe main result of this paper is the construction of a family of superintegrable Hamiltonian systems on moduli spaces of flat connections on a principal G-bundle on a surface. The moduli space is a Poisson variety with Atiyah–Bott Poisson structure. Among particular cases of such systems are spin generalizations of Ruijsenaars–Schneider models.

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