Corpus ID: 198179977

Super McShane identity

@article{Huang2019SuperMI,
  title={Super McShane identity},
  author={Yi Huang and Robert C. Penner and Anton M. Zeitlin},
  journal={arXiv: Geometric Topology},
  year={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 these surfaces and establish asymptotic growth rate of their length spectra. 

Figures from this paper

An Expansion Formula for Decorated Super-Teichmüller Spaces
Motivated by the definition of super-Teichmüller spaces, and Penner–Zeitlin’s recent extension of this definition to decorated super-Teichmüller space, as examples of super Riemann surfaces, we useExpand
Super Hyperbolic Law of Cosines: same formula with different content
We derive the Laws of Cosines and Sines in the super hyperbolic plane using Minkowski supergeometry and find the identical formulae to the classical case, but remarkably involving differentExpand
Towards Super Teichm\"uller Spin TQFT
The quantization of the Teichm\"uller theory has led to the formulation of the so-called Teichm\"uller TQFT for 3-manifolds. In this paper we initiate the study of "supersymmetrization" of theExpand
Volumes And Random Matrices
This article is an introduction to newly discovered relations between volumes of moduli spaces of Riemann surfaces or super Riemann surfaces, simple models of gravity or supergravity in twoExpand

References

SHOWING 1-10 OF 37 REFERENCES
On Ramond Decorations
We impose constraints on the odd coordinates of super-Teichmüller space in the uniformization picture for the monodromies around Ramond punctures, thus reducing the overall odd dimension to beExpand
McShane identities for Higher Teichm\"uller theory and the Goncharov-Shen potential
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 mirrorExpand
Identities on Hyperbolic Manifolds
In this survey, we discuss four classes of identities due principally to Basmajian, McShane, Bridgeman-Kahn and Luo-Tan on hyperbolic manifolds and provide a unified approach for proving them. WeExpand
N=2 super-Teichmüller theory
Abstract Based on earlier work of the latter two named authors on the higher super-Teichmuller space with N = 1 , a component of the flat O S p ( 1 | 2 ) connections on a punctured surface, here weExpand
The decorated Teichmüller space of punctured surfaces
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. SeveralExpand
Markoff triples and quasifuchsian groups
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 PSL(2, C). InExpand
Notes on super Riemann surfaces and their moduli
  • E. Witten
  • Physics, Mathematics
  • Pure and Applied Mathematics Quarterly
  • 2019
These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNSExpand
Weil-Petersson volumes and intersection theory on the moduli space of curves
In this paper, we establish a relationship between the Weil-Petersson volume Vgin(b) of the moduli space Mg,n(b) of hyperbolic Riemann surfaces with geodesic boundary components of lengths b\,...,bn,Expand
Moduli of Riemann Surfaces, Real Algebraic Curves, and Their Superanalogs
Introduction Moduli of Riemann surfaces, Hurwitz type spaces and their superanalogs Moduli of real algebraic curves and their superanalogs. Differentials, spinors, and Jacobians of real curves SpacesExpand
Universal Constructions in Teichmüller Theory
We study a new model Tess of a universal Teichmuller space, which is defined to be the collection Tess′ of all ideal tesselations of the Poincare disk (together with a distinguished oriented edge)Expand
...
1
2
3
4
...