Related papers: Super McShane identity
We derive an identity for Margulis invariants of affine deformations of a complete orientable one-ended hyperbolic sur- face following the identities of McShane, Mirzakhani and Tan- Wong-Zhang. As a corollary, a deformation of the surface…
We prove a McShane-type identity - a series, expressed in terms of geodesic lengths, that sums to 2\pi for any closed hyperbolic surface with one distinguished point. To do so, we prove a generalized Birman-Series theorem showing that the…
We derive generalizations of McShane's identity for higher ranked surface group representations by studying a family of mapping class group invariant functions introduced by Goncharov and Shen which generalize the notion of horocycle…
We generalize McShane's identity for the length series of simple closed geodesics on a cusped hyperbolic surface to hyperbolic cone-surfaces (with all cone angles $\le \pi$), possibly with cusps and/or geodesic boundary. In particular, by…
In this paper we study McShane's identity in real and complex hyperbolic spaces and obtain various generalizations of the identity for representations of surface groups into the isometry groups of rank one symmetric spaces. Our methods…
We introduce a new method to establish McShane's Identity, based upon the fact that elliptic elements of order two in the Fuchsian group uniformizing the quotient of a fixed once-punctured hyperbolic torus act so as to exclude points as…
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 projective structures analogous to Basmajian's…
We survey some of our recent results on length series identities for hyperbolic (cone) surfaces, possibly with cusps and/or boundary geodesics; classical Schottky groups; representations/characters of the one-holed torus group to $SL(2,…
In this paper, a Riemannian geometry of noncommutative super surfaces is developed which generalizes [4] to the super case. The notions of metric and connections on such noncommutative super surfaces are introduced and it is shown that the…
We show that the length spectrum metric on Teichm\"uller spaces of surfaces of infinite topological type is complete. We also give related results and examples that compare the length spectrum Teichm\"uller space with quasiconformal and the…
We give an identity involving sums of functions of lengths of simple closed geodesics, known as a McShane identity, on any non-orientable hyperbolic surface with boundary which generalises Mirzakhani's identities on orientable hyperbolic…
This is the first in a series of papers where we develop new structural elements on singular area minimizing hypersurfaces, the skin structures. They disclose previously unapproachable and largely unexpected geometric and analytic…
Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…
We give a new formula for the Chern-Schwartz-MacPherson class of a hypersurface in a nonsigular compact complex analytic variety. In particular this formula generalizes our previous result on the Euler characteristic of such a hypersurface.…
We show that Norbury's McShane identity for nonorientable cusped hyperbolic surfaces N generalizes to quasifuchsian representations of pi_1(N) as well as pseudo-Anosov mapping Klein bottles with singular fibers given by N.
Given a surface of infinite topological type, there are several Teichm\"uller spaces associated with it, depending on the basepoint and on the point of view that one uses to compare different complex structures. This paper is about the…
We generalise in this article the Mc Shane-Mirzakhani identities in hyperbolic geometry to arbitrary cross ratios. We give an expression of them in the case of Hitchin representations of surface groups in PSL(n, R) in a suitable choice of…
This article provides a brief discussion of the functional of super Riemann surfaces from the point of view of classical (i.e. not "super-) differential geometry. The discussion is based on symmetry considerations and aims to clarify the…
We show that Thurston's skinning maps of Teichmuller space have finite fibers. The proof centers around a study of two subvarieties of the SL_2(C) character variety of a surface, one associated to complex projective structures and the other…
Motivated by the definition of super-Teichm\"uller spaces, and Penner-Zeitlin's recent extension of this definition to decorated super-Teichm\"uller space, as examples of super Riemann surfaces, we use the super Ptolemy relations to obtain…