Fuchsian groups, finite simple groups and representation varieties

By Martin W. Liebeck, Aner Shalev. 2005

94 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e1bfa9a00e23e215b57c1cd838ba602765aabf46

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Jason E. Fulman
2. Robert M. Guralnick
3. Shelly Garion
4. Aner Shalev
5. Tamás Hausel
6. Nir Avni
7. Avraham Aizenbud
8. Fernando Rodriguez-Villegas

In Geometry and Topology

1. Tamás Hausel
2. Jason E. Fulman
3. Shelly Garion
4. Robert M. Guralnick
5. Fernando Rodriguez-Villegas
6. Aner Shalev
7. Nir Avni
8. Avraham Aizenbud

In Mathematical Physics

1. Robert M. Guralnick
2. Tamás Hausel
3. Shelly Garion
4. Aner Shalev
5. Jason E. Fulman
6. Nir Avni
7. Fernando Rodriguez-Villegas
8. Avraham Aizenbud

Citations in the corpus

• Commutator maps, measure preservation, and T-systems (2007, methodology): “Indeed, by Theorem 1.1 of [LiSh4], if G is simple, then It follows that for finite simple groups G , δ ( G ) and (cid:2) ( G ) tend to zero as | G | → ∞ .”
• Representation growth and rational singularities of the moduli space of local systems (2013, background): “This proof, like the one in [36] and unlike the proof in [37] works only in characteristic 0.”
• Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements (2009, methodology): “(4) Liebeck and Shalev [ LS1 ] have used bounds in the current paper to study probabilistic results about homomorphisms of certain Fuchsian groups into Chevalley groups, and random walks on Chevalley groups [LS2].”
• Mixed Hodge polynomials of character varieties (2006, background): “The asymptotics for these numbers as n tends to infinity has been studied in [48].”
• Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks (2004, unknown): “In a subsequent paper [ 30 ] we extend various parts of Theorem 1.12 to all finite simple groups.”
• Determining Fuchsian groups by their finite quotients (2014, background): “Thus, for us, every Fuchsian group Γ has a subgroup of finite index that maps onto a non-abelian free group, and hence every finitely-generated group is a quotient of some finite-index subgroup of Γ. Deciding which groups arise as quotients of Γ itself is a more subtle matter, but much progress has…”