3. The isomorphism problem
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Problem 3.1.
Is the class of spherical Artin groups closed under isomorphism? In other words, if an Artin group A is isomorphic to a spherical Artin group, must A be spherical? -
Problem 3.2.
Solve the isomorphism problem for 2-dimensional Artin groups. -
Problem 3.3.
Solve the isomorphism problem for \infty-free 2-dimensional Artin groups. -
Problem 3.4.
Find the commensurability and Q.I. classification for \infty-free Artin groups.
A specific case: are F_4 and H_4 commensurable? -
Problem 3.5.
For an Artin group A, when is \mathrm{Out}(A) finite/finitely generated? Find explicit generators. -
Problem 3.6.
For an Artin group A, which Artin groups A' embed in A such that A' is not a parabolic subgroup? -
Problem 3.8.
Classify \mathrm{End}(A).
Cite this as: AimPL: Geometry and topology of Artin groups, available at http://aimpl.org/geomartingp.