Department of Mathematics

Geometry and Topology

  •  Robert Bell, MSU
  •  Quasi-positivity in free groups and braid groups
  •  04/18/2019
  •  2:00 PM - 3:00 PM
  •  C304 Wells Hall

I'll discuss joint work with Rita Gitik (UM) on the problem of recognizing quasi-positive elements of a group G defined by a finite presentation (X ; R). An element of G is quasi-positive if it can be represented by a word that is a product of conjugates of positive powers of letters in X. The recognition problem is to determine whether or not a given word (using both positive and negative powers of letters in X) represents an element of G that is quasi-positive. This problem was solved by Orevkov when G is free with basis X or when G is the 3-strand braid group with its standard generating set. I'll present a new solution to the recognition problem for free groups and discuss some of the challenges posed by braid groups and related groups.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science