최서영 교수

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The deformation space C(L) of convex RP2-structures on a closed surface I with #(5)) < 0 is closed in the space Hom(7t, SL(3, R))/SL(3, R) of equivalence classes of representations nx (Z) - SL(3, R).Using this fact, we prove Hitchin's conjecture that the contractible "Teichmiiller component" (Lie groups and Teichmiiller space, preprint) of Homfw, SL(3, R))/SL(3, R) precisely equals C(2).Let X be a closed orientable surface of genus g > 1 and n = nx(L) its fundamental group.A convex EP2-structure

We determine that the deformation space of convex real projective structures, that is, projectively flat torsion-free connections with the geodesic convexity property on a compact 2-orbifold of negative Euler characteristic is homeomorphic to a cell of certain dimension. The basic techniques are from Thurston's lecture notes on hyperbolic 2-orbifolds, the previous work of Goldman on convex real projective structures on surfaces, and some classical geometry.

Real projective structures ($\mathbb {RP}$-structures) on compact surfaces are classified. The space of projective equivalence classes of real projective structures on a closed orientable surface of genus $g>1$ is a countable disjoint union of open cells of dimension $16g-16$. A key idea is Choi’s admissible decomposition of a real projective structure into convex subsurfaces along closed geodesics. The deformation space of convex structures forms a connected component in the moduli space of r

A real projective surface is a differentiable surface with an atlas of charts to real projective plane RP 2 such that transition functions are restrictions of projective automorphisms of RP 2 .Let be an orientable compact real projective surface with convex boundary and negative Euler characteristic.Then uniquely decomposes along mutually disjoint imbedded closed projective geodesies into compact subsurfaces that are maximal annuli, trivial annuli, or maximal purely convex real projective surfac

A real protective surface is a surface with a flat real projective structure. A -annulus is an easy-to-construct real projective annulus with geodesic boundary. Let be an orientable compact real projective surface with convex boundary and negative Euler characteristic. We prove that there is a -annulus with a projective map to whenever is not convex.

This book exposes the connection between the low-dimensional orbifold theory and geometry that was first discovered by Thurston in 1970s providing a key tool in his proof of the hyperbolization of Haken 3-manifolds. Our main aims are to explain most of the topology of orbifolds but to explain the geometric structure theory only for 2-dimensional orbifolds, including their Teichmüller (Fricke) spaces. We tried to collect the theory of orbifolds scattered in various literatures for our purposes. H

One could conjecture that many 3-manifolds admit real projective structures although we do not even have a clue how to go about studying such a question.

We show that Margulis spacetimes without parabolic holonomy elements are topologically tame. A Margulis spacetime is the quotient of the 3-dimensional Minkowski space by a free proper isometric action of the free group of rank 2. We will use our particular point of view that the Margulis spacetime is a manifold-with-boundary with an RP 3 -structure in an essential way. The basic tools are a bordification by a closed RP 2 -surface with free holonomy group, and the work of Goldman, Labourie, and M

International audience

The purpose of our research is to understand geometric and topolog­ ical aspects of real projective structures on surfaces. A real projective surface is a differentiable surface with an atlas of charts to Rp2 such that transition functions are restrictions of projective automorphisms of Rp2. Since such an atlas lifts projective geometry on RP2 to the surface locally and consistently, one can study the global projective geometry of surfaces. This paper is the final piece of the series of the pape