Computer Bounds for Kronheimer-Mrowka Foam Evaluation

Computer Bounds for Kronheimer-Mrowka Foam Evaluation

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David Boozer, University of California, Los Angeles

Zoom link:

https://princeton.zoom.us/j/453512481

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 combinatorial 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.