Remarks on Topological Rigidity of Real Moment-Angle Manifolds
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911600659660800 |
|---|---|
| author | Gkeneralis, Ioannis |
| author_facet | Gkeneralis, Ioannis |
| contents | We study topological rigidity of real moment-angle manifolds associated to flag simplicial complexes. Using the cubical geometry arising from the Davis construction, we identify the universal cover with the Davis complex and deduce that it admits a CAT(0) metric. As a consequence, its fundamental group satisfies the Farrell--Jones conjecture. Applying surgery theory, we deduce that real moment-angle manifolds of dimension at least five associated to flag complexes satisfy the Borel Conjecture. We also explain why this rigidity phenomenon is specific to the real case and fails for complex and quaternionic moment-angle complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15462 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Remarks on Topological Rigidity of Real Moment-Angle Manifolds Gkeneralis, Ioannis Geometric Topology Algebraic Topology 57S25, 57R67, 20F67, 55U10, 51F15 We study topological rigidity of real moment-angle manifolds associated to flag simplicial complexes. Using the cubical geometry arising from the Davis construction, we identify the universal cover with the Davis complex and deduce that it admits a CAT(0) metric. As a consequence, its fundamental group satisfies the Farrell--Jones conjecture. Applying surgery theory, we deduce that real moment-angle manifolds of dimension at least five associated to flag complexes satisfy the Borel Conjecture. We also explain why this rigidity phenomenon is specific to the real case and fails for complex and quaternionic moment-angle complexes. |
| title | Remarks on Topological Rigidity of Real Moment-Angle Manifolds |
| topic | Geometric Topology Algebraic Topology 57S25, 57R67, 20F67, 55U10, 51F15 |
| url | https://arxiv.org/abs/2604.15462 |