Exotic non-orientable four-manifolds with prescribed fundamental group
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914006895165440 |
|---|---|
| author | Torres, Rafael |
| author_facet | Torres, Rafael |
| contents | We show that any finitely presented group with an index two subgroup is realized as the fundamental group of a closed smooth non-orientable four-manifold that admits an exotic smooth structure, which is obtained by performing a Gluck twist. The orientation 2-covers of these four-manifolds are diffeomorphic. These two smooth structures remain inequivalent after adding arbitrarily many copies of the product of a pair of 2-spheres and stabilize after adding a single copy of the complex projective plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exotic non-orientable four-manifolds with prescribed fundamental group Torres, Rafael Geometric Topology Differential Geometry We show that any finitely presented group with an index two subgroup is realized as the fundamental group of a closed smooth non-orientable four-manifold that admits an exotic smooth structure, which is obtained by performing a Gluck twist. The orientation 2-covers of these four-manifolds are diffeomorphic. These two smooth structures remain inequivalent after adding arbitrarily many copies of the product of a pair of 2-spheres and stabilize after adding a single copy of the complex projective plane. |
| title | Exotic non-orientable four-manifolds with prescribed fundamental group |
| topic | Geometric Topology Differential Geometry |
| url | https://arxiv.org/abs/2508.19142 |