A cut-and-paste mechanism to introduce fundamental group and construct new four-manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911471005335552 |
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| author | Bais, Valentina Torres, Rafael |
| author_facet | Bais, Valentina Torres, Rafael |
| contents | We introduce a simple cut-and-paste mechanism to construct both orientable and nonorientable four-manifolds from a given initial one. This mechanism alters the fundamental group while preserving other essential topological invariants. It avoids codimension two cut-and-paste fundamental group computations and fast tracks the search for fixed-point free involutions. The mechanism proves useful to unveil novel exotic irreducible smooth structures on closed four-manifolds with finite cyclic fundamental group, which include $\Q$-homology real projective four-spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23167 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A cut-and-paste mechanism to introduce fundamental group and construct new four-manifolds Bais, Valentina Torres, Rafael Geometric Topology We introduce a simple cut-and-paste mechanism to construct both orientable and nonorientable four-manifolds from a given initial one. This mechanism alters the fundamental group while preserving other essential topological invariants. It avoids codimension two cut-and-paste fundamental group computations and fast tracks the search for fixed-point free involutions. The mechanism proves useful to unveil novel exotic irreducible smooth structures on closed four-manifolds with finite cyclic fundamental group, which include $\Q$-homology real projective four-spaces. |
| title | A cut-and-paste mechanism to introduce fundamental group and construct new four-manifolds |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2505.23167 |