The word problem for quandles

02/21/2012 - 12:15pm
02/21/2012 - 1:10pm
Rena Levitt (Pomona College)

In 1911 Max Dehn stated his now famous word problem: given a finitely generated group G is there an algorithm to determine if two words in the generators represent the same element in G? While algorithms exist for many groups, in the 1950's Novikov and Boone separately provided examples of groups for which the word problem is unsolvable. This leads to the following question: can the word problem be generalized to other algebraic constructions such as quandles? In this talk, I will discuss a natural generalization of Dehn's problem to finitely generated quandles, and show that the word problem is solvable for both free and knot-like quandles. The algorithm we define is similar to Dehn's original method for the fundamental groups of surfaces with genus at least two. This is joint work with Sam Nelson.

Millikan 208 (Pomona College)