Topological classification of certain nonorientable 4-manifolds with cyclic fundamental group of order 2 mod 4
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908754073616384 |
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| author | Torres, Rafael |
| author_facet | Torres, Rafael |
| contents | We show that the classification up to homeomorphism of closed topological nonorientable 4-manifolds with fundamental group of order 2 due to Hambleton-Kreck-Teichner can be used to classify a large set of such 4-manifolds with cyclic fundamental group of order 2p for every odd $p > 1$. This is done through a simple cut-and-paste construction, and classical and modified surgery theory are used only through results of Hambleton-Kreck-Teichner and Khan. It is plausible that this set comprises all closed topological nonorientable 4-manifolds with $π_1 = \Z/2p$. We collect several interesting questions whose answers would guarantee a complete classification. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_05132 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological classification of certain nonorientable 4-manifolds with cyclic fundamental group of order 2 mod 4 Torres, Rafael Geometric Topology 57K40 We show that the classification up to homeomorphism of closed topological nonorientable 4-manifolds with fundamental group of order 2 due to Hambleton-Kreck-Teichner can be used to classify a large set of such 4-manifolds with cyclic fundamental group of order 2p for every odd $p > 1$. This is done through a simple cut-and-paste construction, and classical and modified surgery theory are used only through results of Hambleton-Kreck-Teichner and Khan. It is plausible that this set comprises all closed topological nonorientable 4-manifolds with $π_1 = \Z/2p$. We collect several interesting questions whose answers would guarantee a complete classification. |
| title | Topological classification of certain nonorientable 4-manifolds with cyclic fundamental group of order 2 mod 4 |
| topic | Geometric Topology 57K40 |
| url | https://arxiv.org/abs/2601.05132 |