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Spaces of Kleinian Groups and Hyperbolic 3-Manifolds

2nd August 2003 to 9th August 2003

Organisers: Caroline Series (Warwick), Yair Minsky (Stony Brook), Makoto Sakuma (Osaka)

Supported by the European Commission, Research DG, Human Potential Programme, High-Level Scientific Conferences - HPCF-2001-00106, the NSF and the Leverhulme Trust

Workshop Theme

This workshop will focus on spaces of Kleinian groups. From the viewpoint of complex dynamics, a space of Kleinian groups is a close analogue of the Mandelbrot set; Bers' simultaneous uniformisation theorem reveals these spaces as an extension of Teichmüller theory; while from the 3-dimensional viewpoint they become deformation spaces of hyperbolic 3-manifolds. Each approach contributes its individual flavour, and our aim is to bring together these diverse threads.

Specific topics to be addressed include: relationships between the analytic, combinatorial and geometric structure of hyperbolic 3-manifolds; topology of deformation spaces and the arrangement of their components; classification of hyperbolic 3-manifolds by asymptotic invariants; complex projective structures; convex hull boundaries; cone manifolds, orbifolds and knot groups; the combinatorial structure of Teichmüller spaces, mapping class groups, and spaces of curves on surfaces; and the challenge of extending recent advances from once punctured tori to higher genus. A particular focus will be the experimental computer graphics which have contributed much to the development of the subject. We anticipate that exploration of these pictures will be formative for new phases of research. The first day of the meeting will be especially focussed on this theme.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons