## 770 Citations

### Invariant functions on Lie groups and Hamiltonian flows of surface group representations

- Mathematics
- 1986

Si π est le groupe fondamental d'une surface orientee fermee S et G est un groupe de Lie satisfaisant des conditions tres generales, alors l'espace Hom (π,G)/G des classes de conjugaison de…

### A note on exceptional groups and Reidemeister torsion

- MathematicsJournal of Mathematical Physics
- 2018

Let Σ be a closed orientable surface of genus at least 2 and G be one of the exceptional groups G2, F4, and E6. The present article considers the set Rep(Σ, G) of G-valued representations from the…

### Action of the Johnson-Torelli group on representation varieties

- Mathematics
- 2010

Let Σ be a compact orientable surface with genus g and n boundary components B = (B1, . . . , Bn). Let c = (c1, . . . , cn) ∈ [−2, 2]n. Then the mapping class group MCG of Σ acts on the relative…

### A Foliation of the Space of Conjugacy Classes of Representations of a Surface Group

- Mathematics
- 2001

Let Π be the fundamental group of a closed orientable surface of genus g ≥ 1, and let R(Π, G)/G be the space of conjugacy classes of representations of Π into a connected real reductive Lie group G.…

### Ergodicity of Mapping Class Group Actions on SU(2)-character varieties

- Mathematics
- 2009

Let S be a compact orientable surface with genus g and n boundary components d_1,...,d_n. Let b = (b_1, ..., b_n) where b_n lies in [-2,2]. Then the mapping class group of S acts on the relative…

### MAPPING CLASS GROUP DYNAMICS ON SURFACE GROUP REPRESENTATIONS

- Mathematics
- 2006

Deformation spaces Hom(�,G)/G of representations of the fundamental groupof a surfacein a Lie group G ad- mit natural actions of the mapping class group Mod�, preserving a Poisson structure. When G…

### INTERSECTION COHOMOLOGY OF REPRESENTATION SPACES OF SURFACE GROUPS

- Mathematics
- 2001

The representation space X(G) = Hom(π, G)/G of the fundamental group π of a Riemann surface Σ of genus g ≥ 2 is the symplectic reduction of the extended moduli space defined in [6]. Using this…

### Non-injective representations of a closed surface group into PSL ( 2 , R ) By

- Mathematics
- 2005

Let e denote the Euler class on the space Hom(Γg, P SL(2, R)) of representations of the fundamental group Γg of the closed surface Σg. Goldman showed that the connected components of Hom(Γg, P SL(2,…

### Covering spaces of character varieties Sean Lawton and

- Mathematics
- 2015

Let Γ be a finitely generated discrete group. Given a covering map H → G of Lie groups with G either compact or complex reductive, there is an induced covering map Hom(Γ, H) → Hom(Γ, G). We show that…

### Gluing Formulas for Volume Forms on Representation Varieties of Surfaces

- Mathematics
- 2022

. Let Σ g,n be a compact oriented surface with genus g ≥ 2 bordered by n circles. Due to Witten, the twisted Reidemeister torsion coincides with a power of the Atiyah-Bott-Goldman-Narasimhan…

## References

SHOWING 1-10 OF 32 REFERENCES

### Characteristic classes and representations of discrete subgroups of Lie groups

- Mathematics
- 1982

A volume invariant is used to characterize those representations of a countable group into a connected semisimple Lie group G which are injective and whose image is a discrete cocompact subgroup of…

### Deformations of homomorphisms of Lie groups and Lie algebras

- Mathematics
- 1967

The purpose of this note is to announce several results on deformations of homomorphisms of Lie groups and Lie algebras. Our main theorems are precise analogues of two basic theorems on deformations…

### Braids, Links, and Mapping Class Groups.

- Mathematics
- 1975

The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with…

### Stable and unitary vector bundles on a compact Riemann surface

- Mathematics
- 1965

Let X be a compact Riemann surface of genus g _ 2. A holomorphic vector bundle on X is said to be unitary if it arises from a unitary representation of the fundamental group of X. We prove in this…

### The Fenchel-Nielsen deformation

- Mathematics
- 1982

The uniformization theorem provides that a Riemann surface S of negative Euler characteristic has a metric of constant curvature -1. A hyperbolic structure can be understood in terms of its…

### On the symplectic geometry of deformations of a hyperbolic surface

- Mathematics
- 1983

Let R be a Riemann surface. In this manuscript we consider a geometry on the moduli space X(R) for R, which we regard as the space of equivalence classes of constant curvature metrics on the…

### Discrete subgroups of Lie groups

- Mathematics
- 1972

Preliminaries.- I. Generalities on Lattices.- II. Lattices in Nilpotent Lie Groups.- III. Lattices in Solvable Lie Groups.- IV. Polycyclic Groups and Arithmeticity of Lattices in Solvable Lie…

### Lectures on Symplectic Manifolds

- Mathematics
- 1977

Introduction Symplectic manifolds and lagrangian submanifolds, examples Lagrangian splittings, real and complex polarizations, Kahler manifolds Reduction, the calculus of canonical relations,…

### The Yang-Mills equations over Riemann surfaces

- MathematicsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- 1983

The Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory. The main result is that this is a ‘perfect' functional provided due account is taken of its gauge…