Related papers: Turaev Surfaces

This article is a very short introduction to pcf theory for topologists.

These are notes from my lecture at 4ECM in Stockholm (June 2004).

In this paper, we describe the relation between the Turaev--Viro TQFT and the string-net space introduced in the papers of Levin and Wen. In particular, the case of surfaces with boundary is considered in detail.

The purpose of this paper is to discuss how topology and geometry provide, in many instances, the connective tissue that enables logical comprehension. We illustrate this theme with many examples including Venn diagrams, knot diagrams,…

This note is an expository account of the theory of staggered sheaves, based on a series of lectures given by the author at RIMS (Kyoto) in October 2008.

This note is withdrawn. The result and its proof are available in the literature.

We revisit Ahlfors theory of covering surfaces thanks to Stokes theorem.

A conjecture regarding the structure of expander graphs is discussed.

In this article we consider exceptional sequences of invertible sheaves on smooth complete rational surfaces. We show that to every such sequence one can associate a smooth complete toric surface in a canonical way. We use this structural…

We give a short proof of Ahlfors' theorem on covering surfaces.

This monograph is on convex real projective structures on strongly tame n-orbifolds with some appropriate conditions on ends.

In the paper, we give a Schur-Toponogov theorem in Riemannian geometry, which not only generalizes Schur's and Toponogov's theorem but also indicates their relation. Inspired by its proof, we also supply a new proof of Toponogov's theorem…

Review paper. Chapter 6 in Janus Particles Synthesis, Self-Assembly, and Applications pages 108-137, Edited by Steve Granick and Shan Jiang (RCS Publishing 2012) http://www.rsc.org/Shop/books/2012/9781849734233.asp

In the present work we are going to give a formal exposition of the ribbon graphs topic based on notes of Labourie \cite{Lab}, since is difficult to find as such in the literature.

In this paper, based on the theory of surfaces in the four-dimensional Euclidean space which generalizes the theory of surfaces in three-dimensional Euclidean space, beside other results, we will give a characterization of points on…

The result of this paper is proved in arXiv:1112.1163

The work provides a brief intuitive overview theory of graph on surfaces. We considers graphs with an additional structure, wich we call discs with ribbons, also known as one-vertex ribbon graphs. And solves the problem (Skopenkov's) about…

In this paper we look at which Alexander and Markov theories can be defined for generalized knot theories

To appear in Encyclopedia of Mathematical Physics, J.-P. Fran\c{c}oise, G. Naber and T.S. Tsou, eds., Elsevier, 2006. The article surveys the modern developments of noncommutative geometry in string theory.

A very interesting problem in the classical theory of minimal surfaces consists of the classification of such surfaces under some geometrical and topological constraints. In this short paper, we give a brief summary of the known…