REPRESENTATION
THEORY AND RELATED TOPICS SEMINAR
ABSTRACT: Picture
groups were introduced last year by Gordana Todorov. These are related
to exceptional sequences and maximal green sequences. The cohomology of
picture groups is related to the cohomology of nilpotent groups. One of
the basic theorems is that, for finite type quivers, the classifying
space of the ``cluster morphism category’’ is a K(π,1) for the picture
group of the quiver. The purpose of this paper is to give an elementary
combinatorial interpretation of the category associated to A_n and to
give a new proof that the classifying space of this category is a
K(π,1) where π is the picture group of type A_n. The objects of the
category are noncrossing partitions. An appendix to the paper is
planned, written jointly with Gordana Todorov, where we show, using a
result of Speyer and Thomas, that all picture groups of finite type are
Cat(0)-groups. This talk will not have the definition of CAT(0) spaces,
exceptional sequences or of maximal green sequences. I will concentrate
on combinatorics and the picture group.
For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html or contact Alex Martsinkovsky alexmart >at< neu >dot< edu