TY  - THES
AB  - The main achievement of this thesis is the construction of a new family of
simplicial complexes interpolating between Tits buildings and free factor complexes.
For every finite graph G, we obtain a simplicial complex CC associated
to the outer automorphism group of the right-angled Artin group A<sub>G</sub>. These
complexes are defined using the intersection patterns of cosets of parabolic subgroups.
Each of them is homotopy Cohen–Macaulay and in particular homotopy
equivalent to a wedge of d-spheres. The dimension d can be read off from the
defining graph G and provides a new invariant for the automorphism group of
A<sub>G</sub>.
In order to deduce this and further properties of CC, we introduce new
methods for studying the topology of coset complexes and coset posets, refine
the decomposition sequence for automorphism groups of right-angled Artin
groups established by Day–Wade and study the asymptotic geometry of Culler–
Vogtmann Outer space. In particular, we show that the simplicial boundary of
the Outer space of the free group F<sub>n</sub> can be described in terms of complexes of
free factors of F<sub>n</sub> and study the connectivity properties of these complexes.
DA  - 2020
LA  - eng
PY  - 2020
TI  - Between buildings and free factor complexes
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29400204
Y2  - 2024-11-22T07:04:31
ER  -