# An action of the cactus group

@article{Henriques2007AnAO, title={An action of the cactus group}, author={Andr{\'e} Henriques}, journal={arXiv: Algebraic Geometry}, year={2007} }

We construct an action of the big cactus group (the fundamental group of the Deligne-Mumford compactification of the moduli space of real curves of genus zero with n undistinguished marked points) on Fock-Goncharov's SL_m analog of the decorated Teichmuller space of ideal n-gons.

## 7 Citations

### CLUSTER STRUCTURES ON HIGHER TEICHMULLER SPACES FOR CLASSICAL GROUPS

- MathematicsForum of Mathematics, Sigma
- 2019

Let $S$ be a surface, $G$ a simply connected classical group, and $G^{\prime }$ the associated adjoint form of the group. We show that the moduli spaces of framed local systems…

### An Approach to to Cluster Structures on Moduli of Local Systems for General Groups

- Mathematics
- 2016

Let $S$ be a surface, $G$ a simply-connected classical group, and $G'$ the associated adjoint form of the group. In \cite{FG1}, it was shown that the moduli spaces of framed local systems $\X_{G',S}$…

### On bases of tropical Pl\"ucker functions

- Mathematics
- 2007

We consider functions f : B → R that obey tropical analogs of classical Plücker relations on minors of a matrix. The most general set B that we deal with in this paper is of the form {x ∈ Z : 0 ≤ x ≤…

### Separated set-systems and their geometric models

- Mathematics
- 2010

This paper discusses strongly and weakly separated set-systems as well as rhombus tilings and wiring diagrams which are used to produce such systems. In particular, the Leclerc-Zelevinsky conjectures…

### On bases of tropical Plücker functions

- Mathematics
- 2007

We consider functions $f:B\to\Rset$ that obey tropical analogs of classical Pl\"ucker relations on minors of a matrix. The most general set $B$ that we deal with in this paper is of the form $\{x\in…

### Braid group symmetries of Grassmannian cluster algebras

- MathematicsSelecta Mathematica
- 2020

Let Gr∘(k,n)⊂Gr(k,n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…

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