2. The word problem
-
Problem 2.2.
Is there an explicit algorithm to solve the word problem for all Artin groups? -
We call an Artin group hyperbolic if the quadratic form of the associated Coxeter group is rank (n, 1).
Problem 2.3.
Find more examples of \geq 3-dimensional hyperbolic Artin groups (whose diagrams have no edges labeled \infty) where the word problem is solvable. -
(See Question 1.4 of [MR2983847] for the algorithm.)
Problem 2.4.
Does Dehornoy-Godelle’s algorithm solve the word problem for all Artin groups? -
Problem 2.5.
If g = a\overline{b} for a,b words in the positive monoid with no cancellation in the middle, are a and b unique?
Cite this as: AimPL: Geometry and topology of Artin groups, available at http://aimpl.org/geomartingp.