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- University of Warwick
- Coventry CV4 7AL
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The resolution of many of Thurston's prophetic questions about the structure of 3-manifolds has generated a vast array of techniques which permeate many of the areas covered by the symposium.
As is often the case, the resolution of old conjectures has led to intriguing new questions, which will be the focus of this workshop. Examples include: given a combinatorial or arithmetic presentation of a 3--manifold, describe its geometric structure concretely (''effective geometrisation''); understand the geometry of the Thurston unit norm ball, for example how it behaves under taking towers of covers; understand the connection between Heegard-Floer homology and orderability of fundamental groups. Several old conjectures, such as the simple loop conjecture for surfaces in three-manifolds and the conjecture that a quasifuchsian group is determined by its pleating laminations, continue to motivate work.
Links with other workshop areas include a renewed focus on computation in 3-manifold theory, the use of special cube complexes via the Agol-Wise machinery, used to resolve several of the conjectures which remained after Perelman's solution to the Geometrisation conjecture, and the geometry and combinatorics of complexes of discs and spheres in 3-manifolds, which have been used to investigate the structure of outer automorphism groups of free groups.
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