Groups and Geometry in the South East
This is a series of meetings at UCL, with the aim of bringing together the geometric group theorists in the South East of England. The meetings are sponsored by mathematicians from the Universities of Cambridge, London, Oxford and Southampton, and organised by Martin Bridson and Henry Wilton. We have been awarded LMS Scheme 3 funding.
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Details of our next meeting will appear below. Note that it will be held at Imperial College, NOT at UCL.
Friday 4th May, 2012
Location: Room 130, Huxley Building, Imperial College London.
2.45pm Realisation and dismantlability
Piotr Przytycki (Warsaw)
This is joint work with S. Hensel and D. Osajda. We give a new proof of the Nielsen Realisation Problem for a punctured surface: any finite subgroup of the mapping class group of a punctured surface acts as isometries of some hyperbolic metric. Our method is to find a fixed clique of the action of the finite group on the arc graph, using its "dismantlability". This approach also shows that the set of fixed points in Harer's spine is contractible. The strategy works for actions on the disc and sphere graphs as well.
4pm Cocompact lattices on A_2-tilde buildings
Anne Thomas (Sydney)
An A_2-tilde building is a CAT(0) polygonal complex which is a union of Euclidean planes tessellated by equilateral triangles. If K is the field of formal Laurent series over a finite field, and G = SL(3,K), then there is an A_2-tilde building X on which G acts with quotient a triangle and compact stabilisers. A cocompact lattice in G is then a group which acts on X cocompactly with finite stabilisers. We construct new cocompact lattices in G and relate them to previous examples. Our methods include extending work of Cartwright, Mantero, Steger and Zappa, which used cyclic simple algebras, and considering the action of finite groups of Lie type on X. This is joint work with Inna Capdeboscq and Dmitri Rumynin.