Scissors automorphism groups II: Solomon-Tits theorems
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917453117784064 |
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| author | Kupers, Alexander Lemann, Ezekiel Malkiewich, Cary Miller, Jeremy Sroka, Robin J. |
| author_facet | Kupers, Alexander Lemann, Ezekiel Malkiewich, Cary Miller, Jeremy Sroka, Robin J. |
| contents | The Solomon-Tits theorem says that the poset of proper non-trivial subspaces of a finite-dimensional vector space has realisation equivalent to a wedge of spheres. In this paper we prove a variant of this result for collections of geodesic subspaces of Euclidean, hyperbolic, or spherical geometry, assuming the collection is generated either by points or by hyperplanes. In the third paper of this series of papers, we will combine this with the homological stability theorems from the first paper to compute the homology of groups of scissors automorphisms in these geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00541 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scissors automorphism groups II: Solomon-Tits theorems Kupers, Alexander Lemann, Ezekiel Malkiewich, Cary Miller, Jeremy Sroka, Robin J. Algebraic Topology Group Theory K-Theory and Homology Representation Theory 20J05, 52C35, 51E24, 52B45, 19D99 The Solomon-Tits theorem says that the poset of proper non-trivial subspaces of a finite-dimensional vector space has realisation equivalent to a wedge of spheres. In this paper we prove a variant of this result for collections of geodesic subspaces of Euclidean, hyperbolic, or spherical geometry, assuming the collection is generated either by points or by hyperplanes. In the third paper of this series of papers, we will combine this with the homological stability theorems from the first paper to compute the homology of groups of scissors automorphisms in these geometries. |
| title | Scissors automorphism groups II: Solomon-Tits theorems |
| topic | Algebraic Topology Group Theory K-Theory and Homology Representation Theory 20J05, 52C35, 51E24, 52B45, 19D99 |
| url | https://arxiv.org/abs/2605.00541 |