On uniqueness of the equivariant smooth structure on a real moment-angle manifold
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910853534580736 |
|---|---|
| author | Erokhovets, Nikolai Erokhovets, Elena |
| author_facet | Erokhovets, Nikolai Erokhovets, Elena |
| contents | The paper is devoted to the well-known problem of smooth structures on moment-angle manifolds. Each real or complex moment-angle manifold has an equivariant smooth structure given by an intersection of quadrics corresponding to a geometric realisation of a polytope. In 2006 F.Bosio and L.Meersseman proved that complex moment-angle manifolds of combinatorially equivalent simple polytopes are equivariantly diffeomorphic. Using arguments from calculus we derive from this result that real moment-angle manifolds of combinatorially equivalent simple polytopes are equivariantly diffeomorphic and the polytopes are diffeomorphic as manifolds with corners. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00446 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On uniqueness of the equivariant smooth structure on a real moment-angle manifold Erokhovets, Nikolai Erokhovets, Elena Geometric Topology Algebraic Topology Differential Geometry 57S12, 57S17, 57S25, 52B05, 52B70, 57R18, 57R91 The paper is devoted to the well-known problem of smooth structures on moment-angle manifolds. Each real or complex moment-angle manifold has an equivariant smooth structure given by an intersection of quadrics corresponding to a geometric realisation of a polytope. In 2006 F.Bosio and L.Meersseman proved that complex moment-angle manifolds of combinatorially equivalent simple polytopes are equivariantly diffeomorphic. Using arguments from calculus we derive from this result that real moment-angle manifolds of combinatorially equivalent simple polytopes are equivariantly diffeomorphic and the polytopes are diffeomorphic as manifolds with corners. |
| title | On uniqueness of the equivariant smooth structure on a real moment-angle manifold |
| topic | Geometric Topology Algebraic Topology Differential Geometry 57S12, 57S17, 57S25, 52B05, 52B70, 57R18, 57R91 |
| url | https://arxiv.org/abs/2503.00446 |