This paper is devoted to recent progress made towards the understanding of closed bosonic
and fermionic string perturbation theory, formulated in a Lorentz-covariant way on Euclidean …

This book offers an easy and compact access to the theory of TeichmA1/4ller spaces,
starting from the most elementary aspects to the most recent developments, eg the role this …

The Complex of Curves on a Surface is a simplicial complex whose vertices are homotopy
classes of simple closed curves, and whose simplices are sets of homotopy classes which …

In this paper we will use methods of Riemann surface theory, particularly that of Teichmdtller
theory, to solve a problem in topological dynamics. We are interested in the piecewise order …

Various problems of geometry, topology and dynamical systems on surfaces as well as
some questions concerning one-dimensional dynamical systems lead to the study of closed …

The main goal of the book is to present a proof of the following. Thurston's Hyperbolization
Theorem (" The Big Monster"). Suppose that M is a compact atoroidal Haken 3-manifold that …

We prove results about orbit closures and equidistribution for the SL (2, ℝ) action on the
moduli space of compact Riemann surfaces, which are analogous to the theory of unipotent …

In this paper, we establish a relationship between the Weil-Petersson volume $ V_ {g, n}(b)
$ of the moduli space $\mathcal {M} _ {g, n}(b) $ of hyperbolic Riemann surfaces with …

We study the bosonization of chiral fermion theories on arbitrary compact Riemann surfaces.
We express the fermionic and bosonic correlation functions in terms of theta functions and …

These lectures review some aspects of the theory of moduli spaces which have recently
become important in string theory. They begin with some elements of complex geometry …