Hebrew University Amitsur Algebra Seminar ***************************** Time: Wednesday, October 26, at 12:00. (Notice that it is on Wednesday and not Thursday) Place: room 209, Mathematics building Speaker: Alexander Rahm Title: Stringy orbifolds Abstract: A fruitful way to understand arithmetic groups, is to see them acting on a cell complex with finite stabilisers. We can express the whole group structure with a finite set of information: the orbifold structure. An interesting example for a 3-dimensional cell complex is hyperbolic 3-space, acted on by the Bianchi groups (the SL_2 matrix groups over the rings of integers in imaginary quadratic number fields, modulo the kernel of the action). A fundamental domain for this action is a single polyhedron, and we can explicitly complete it to an orbifold structure (containing additionally the stabilisers and identifications). An innovation in the study of arithmetic groups comes with the recently introduced technique of torsion subcomplex reduction. The latter investigates and reduces the subcomplexes which we obtain from the fundamental polytope by extracting the facets with elements of a given order in their stabiliser. This has helped to understand a correspondence between the homeomorphism type of the torsion subcomplex and the group homology with coefficients modulo the element order in question. The significance of this correspondence is illustrated in the proof of recently found formulae for the dimensions of the Chen/Ruan stringy orbifold cohomology on our class of orbifolds, in terms of elementary number-theoretic information. We complete the picture by a general description of the Chen/Ruan orbifold cohomology product for all groups generated by translations and rotations of complex hyperbolic space. You are cordially invited! <http://math.huji.ac.il/amitsur.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Gili Schul <gili.schul@mail.huji.ac.il>