AN UPPER BOUND ON THE DEHN FUNCTION OF Out(AΓ)

AN UPPER BOUND ON THE DEHN FUNCTION OF Out(AΓ)

Mathematics

Geometric Group Theory (Maths)

Jakub Tucker

2024

To obtain an upper bound on the Dehn function of the outer automorphism group Out0 (AΓ) for a right-angled Artin group AΓ with defining graph Γ, we use the subnormal series defined by Day and Wade in [2 ] to decompose Out0 (AΓ). This yields a decomposition tree where each vertex G has two descendants N and Q, satisfying a short exact sequence 1 → N → G → Q → 1 We prove an upper bound for the Dehn function of the group G in relation to the Dehn functions of the groups N and Q. The Dehn functions of the leaves of the decomposition tree are known, with these we can bound above the Dehn function of their root, and by extension that of the group Out0 (AΓ)

Geometric Group Theory, Group Theory, Maths, Dehn Function, Right-angled Artin Group, Algebra