NORTHEASTERN UNIVERSITY
MATHEMATICS DEPARTMENT

REPRESENTATION THEORY AND RELATED TOPICS SEMINAR


  Kiyoshi Igusa
(Waltham)


Category of Noncrossing Partitions

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.


September 12, 2014
10:30 - 11:30
511 Lake Hall


For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html  or contact Alex Martsinkovsky alexmart >at< neu >dot< edu