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2. The word problem


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      Problem 2.1.

      Is the word problem solvable for all Artin groups?


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          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 $(n, 1)$.

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              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.
                  Some examples in 3 and 4 dimensions by Haettel-Huang

                •     (See Question 1.4 of [MR2983847] for the algorithm.)

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                  Problem 2.4.

                  Does Dehornoy-Godelle’s algorithm solve the word problem for all Artin groups?
                      Known for FC-type


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                      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.