• Corpus ID: 118682769

# McShane identities for Higher Teichm\"uller theory and the Goncharov-Shen potential

@article{Huang2019McShaneIF,
title={McShane identities for Higher Teichm\"uller theory and the Goncharov-Shen potential},
author={Yi Huang and Zhe Sun},
journal={arXiv: Geometric Topology},
year={2019}
}
• Published 7 January 2019
• Mathematics
• arXiv: Geometric Topology
In [GS15], Goncharov and Shen introduce a family of mapping class group invariant regular functions on their $\mathcal{A}$-moduli space to explicitly formulate a particular homological mirror symmetry conjecture. Using these regular functions, we obtain McShane identities general rank positive surface group representations with loxodromic boundary monodromy and (non-strict) McShane-type inequalities for general rank positive representations with unipotent boundary monodromy. Our identities are…
19 Citations
• Mathematics
• 2020
In a companion paper [DS20] we constructed non-negative integer coordinates ΦT for a distinguished collection W3,Ŝ of SL3-webs on a finite-type punctured surface Ŝ, depending on an ideal
These are notes on the hyperbolic geometry of surfaces, Teichmüller spaces and Thurston’s metric on these spaces. They are associated with lectures I gave at the Morningside Center of Mathematics of
The rank n swapping algebra is a Poisson algebra defined on the set of ordered pairs of points of the circle using linking numbers, whose geometric model is given by a certain subspace of (Kn ×
• Mathematics
• 2020
For a finite-type surface $\mathfrak{S}$, we study a preferred basis for the commutative algebra $\mathbb{C}[\mathcal{X}_{\mathrm{SL}_3(\mathbb{C})}(\mathfrak{S})]$ of regular functions on the
For the moduli space of unmarked convex $\mathbb{RP}^2$ structures on the surface $S_{g,m}$ with negative Euler characteristic, we investigate the subsets of the moduli space defined by the notions
• J. Kruthoff
• Mathematics
Journal of High Energy Physics
• 2022
We propose a generalization of the Saad-Shenker-Stanford duality relating matrix models and JT gravity to the case in which the bulk includes higher spin fields. Using a PSL(N, ℝ) BF theory we
Nigel Hitchin [54] used the theory of Higgs bundles to exhibit a component of the “character variety” of (conjugacy classes of) representations of a closed surface group into PSL(d,R) which is
• Mathematics
Geometriae Dedicata
• 2021
We study Thurston’s Lipschitz and curve metrics, as well as the arc metric on the Teichmüller space of one-hold tori equipped with complete hyperbolic metrics with boundary holonomy of fixed length.
In this semi-expository article we describe a gluing method developed for constructing certain model objects in representation varieties Hom (π1 (Σ) , G) for a topological surface Σ and a semisimple
• Mathematics
• 2019
The authors derive a McShane identity for once-punctured super tori. Relying upon earlier work on super Teichm\"uller theory by the last two-named authors, they further develop the supergeometry of

## References

SHOWING 1-10 OF 96 REFERENCES

• Mathematics
• 2015
We prove an extension of Basmajian's identity to n ‐Hitchin representations of compact bordered surfaces. For n=3 , we show that this identity has a geometric interpretation for convex real
• Mathematics
• 2004
In [15], Greg McShane demonstrated a remarkable identity for the lengths of simple closed geodesics on cusped hyperbolic surfaces. This was generalized by the authors in [19] to hyperbolic
• Mathematics
• 2003
Let G be a split semisimple algebraic group over Q with trivial center. Let S be a compact oriented surface, with or without boundary. We define positive representations of the fundamental group of S
We adapt Bers' double uniformization for nonorientable surfaces and show that the space $\mathcal{QF}(N)$ of quasifuchsian representations for a nonorientable surface $N$ is the Teichm\"uller space
A principal ℝ+5-bundle over the usual Teichmüller space of ans times punctured surface is introduced. The bundle is mapping class group equivariant and admits an invariant foliation. Several
We study the global behaviour of trees of Markoff triples over the complex numbers. We relate this to the space of type‐preserving representations of the punctured torus group into SL(2,C). In
• Mathematics
• 2013
The action of the mapping class group of the thrice-punctured projective plane on its $$\mathop {\mathrm{GL}}\nolimits (2,{\mathbb {C}})$$GL(2,C) character variety produces an algorithm for
Finitely generated groups and actions of finitely generated groups often come up in studying topology and geometry. While the most important example may be as fundamental groups of compact manifolds,
The rank n swapping algebra is a Poisson algebra defined on the set of ordered pairs of points of the circle using linking numbers, whose geometric model is given by a certain subspace of (Kn ×
• Mathematics
• 2014
We construct a geometric, real analytic parametrization of the Hitchin component Hit_n(S) of the PSL_n(R)-character variety R_{PSL_n(R)}(S) of a closed surface S. The approach is explicit and