A contractible complex generalizing the McCullough-Miller space is constructed for pure symmetric automorphism groups of right-angled Artin groups, with applications to cohomological dimension and l2-cohomology.
Relative Untwisted Outer Space for Right-Angled Artin Groups
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abstract
For G, H two finite collections of finitely generated subgroups of a right-angled Artin group A, the untwisted McCool group U(A; G, Ht) is the subgroup of untwisted outer automorphisms of A preserving the conjugacy class of each element of G and acting trivially up to conjugacy on each element of H. We prove that when the elements of G are standard subgroups of A, U(A; G, Ht) acts properly cocompactly on a finite-dimensional subcomplex of the spine of untwisted outer space for A, providing a geometric model for this group and proof that it is of type VF.
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The McCullough-Miller complex for right angled Artin groups
A contractible complex generalizing the McCullough-Miller space is constructed for pure symmetric automorphism groups of right-angled Artin groups, with applications to cohomological dimension and l2-cohomology.