Graphical complexes of groups
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Tomasz Prytuła
Abstract
We introduce graphical complexes of groups, which can be thought of as a generalisation of Coxeter systems with 1-dimensional nerves.
We show that these complexes are strictly developable, and we equip the resulting Basic Construction with three structures of non-positive curvature: piecewise linear
Funding source: H2020 Marie Skłodowska-Curie Actions
Award Identifier / Grant number: 713683
Funding statement: I was supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 713683.
Acknowledgements
I would like to thank Damian Osajda and Jacek Świa̧tkowski for helpful discussions. I thank Aleksander Pedersen Prytuła for his assistance during this work. I would like to thank the anonymous referee for many valuable remarks. I also thank the Max Planck Institute for Mathematics where part of the work was completed.
Communicated by: Dessislava Kochloukova
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Articles in the same Issue
- Frontmatter
- Presentations of Schur covers of braid groups
- Graphical complexes of groups
- Narrow normal subgroups of Coxeter groups and of automorphism groups of Coxeter groups
- A closure operator on the subgroup lattice of GL(𝑛,𝑞) and PGL(𝑛,𝑞) in relation to the zeros of the Möbius function
- On the strong connectivity of the 2-Engel graphs of almost simple groups
- Finitely generated metabelian groups arising from integer polynomials
- Finite 𝑝-groups of class two with a small multiple holomorph
- Hall classes in linear groups
- Projective representations of Heisenberg groups over the rings of order 𝑝2
Articles in the same Issue
- Frontmatter
- Presentations of Schur covers of braid groups
- Graphical complexes of groups
- Narrow normal subgroups of Coxeter groups and of automorphism groups of Coxeter groups
- A closure operator on the subgroup lattice of GL(𝑛,𝑞) and PGL(𝑛,𝑞) in relation to the zeros of the Möbius function
- On the strong connectivity of the 2-Engel graphs of almost simple groups
- Finitely generated metabelian groups arising from integer polynomials
- Finite 𝑝-groups of class two with a small multiple holomorph
- Hall classes in linear groups
- Projective representations of Heisenberg groups over the rings of order 𝑝2
