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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.15457 |
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| _version_ | 1866915014890225664 |
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| author | Sahattchieve, Jordan A. |
| author_facet | Sahattchieve, Jordan A. |
| contents | This article contains a proof of the fact that, under certain mild technical conditions, the action of the automorphism group of a cyclic 3-manifold cover of the type SxR, where S is a compact surface, yields a compact quotient. This result is then immediately applied to extend a theorem on the fiberings over the circle of certain compact 3-manifolds which are torus sums. As a corollary, I prove the validity of the conditional main theorem in my article titled "A fibering theorem for 3-manifolds", which appeared in the Journal of Groups, Complexity, Cryptology in 2021 and its subsequent erratum. This paper also furnishes a proof of the irreducibility of the summands of compact 3-manifolds which are torus sums and irreducible, and a proof of the interesting observation that a compact connected orientable 3-manifold whose fundamental group contains a subnormal subgroup of infinite index is the connected sum of an irreducible compact 3-manifold with (finitely many) 3-balls. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the cyclic 3-manifold covers of the type surface x R Sahattchieve, Jordan A. General Mathematics 57K30, 57M07, 57M10, 57M60 This article contains a proof of the fact that, under certain mild technical conditions, the action of the automorphism group of a cyclic 3-manifold cover of the type SxR, where S is a compact surface, yields a compact quotient. This result is then immediately applied to extend a theorem on the fiberings over the circle of certain compact 3-manifolds which are torus sums. As a corollary, I prove the validity of the conditional main theorem in my article titled "A fibering theorem for 3-manifolds", which appeared in the Journal of Groups, Complexity, Cryptology in 2021 and its subsequent erratum. This paper also furnishes a proof of the irreducibility of the summands of compact 3-manifolds which are torus sums and irreducible, and a proof of the interesting observation that a compact connected orientable 3-manifold whose fundamental group contains a subnormal subgroup of infinite index is the connected sum of an irreducible compact 3-manifold with (finitely many) 3-balls. |
| title | On the cyclic 3-manifold covers of the type surface x R |
| topic | General Mathematics 57K30, 57M07, 57M10, 57M60 |
| url | https://arxiv.org/abs/2406.15457 |