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>
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Gili Schul   <gili.schul@mail.huji.ac.il>