GEOMETRY and TOPOLOGY Seminar

SPEAKER:  David Boozer  (UCLA)

TITLE:  Computer Bounds for Kronheimer-Mrowka Foam Evaluation

ABSTRACT:

Kronheimer and Mrowka recently suggested a possible approach towards a new proof of the four color theorem that does not rely on computer calculations. One outgrowth of their approach is the definition of a functor J^flat from the category of webs and foams to the category of integer-graded vector spaces over the field of two elements. Of particular interest is the relationship between the dimension of J^flat (K) for a web K and the number of Tait colorings Tait(K) of K.  I describe a computer program that strongly constrains the possibilities for the dimension and graded dimension of J^flat(K) for a given web K, in many cases determining these quantities uniquely.