6533b7d8fe1ef96bd1269b5a

RESEARCH PRODUCT

Teichmuller Space and Related Topics : Proceedings of the workshop on Geometry, January 20, 2011, JOSAI UNIVERSITY

Athanase PapadopoulosGuillaume Théret

subject

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Mathematics - Geometric Topologyhyperbolic structureTeichmüller spaceTeichmuller space32G15 ; 30F30 ; 30F60[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]FOS: MathematicsGeometric Topology (math.GT)measured foliationhexagon[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]

description

The theory of geometric structures on a surface with nonempty boundary can be developed by using a decomposit,ion of such a surface into hexagons, in the same way as the theory of geometric structures on a surface without boundary is developed using the decomposition of such a surface into pairs of pants. The basic elements of the theory for surfaces with boundary include the study of measured foliations and of hyperbolic structures on hexagons. It turns out that there is an interesting space of measured foliations on a hexagon, which is equipped with a piecewise-Iinear structure (in fact, a natural cell-decomposition), and this space is a natural boundary for the space of hyperbolic structures with geodesic boundary and rjght angles on such a hexagon. In this paper, we describe these spaces and the related structures.

yearjournalcountryeditionlanguage
2012-01-01
https://dx.doi.org/10.48550/arxiv.1210.0219