Real Bott manifold structure of $n$-dimensional Klein bottle and its rational Betti numbers
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866910908557557760 |
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| author | Daundkar, Navnath Deshpande, Priyavrat |
| author_facet | Daundkar, Navnath Deshpande, Priyavrat |
| contents | Donald Davis initiated the study of an $n$-dimensional analogue of the Klein bottle. This generalized Klein bottle occurs as a moduli space of planar polygons for a certain choice of side lengths. In this paper, we show that the $n$-dimensional Klein bottle is a real Bott manifold and determine the corresponding Bott matrix. We determine the small cover structure on two other classes of moduli spaces of planar polygons. As an application, we compute the rational Betti numbers of these spaces using a formula, due to Suciu and Trevisan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_01063 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Real Bott manifold structure of $n$-dimensional Klein bottle and its rational Betti numbers Daundkar, Navnath Deshpande, Priyavrat Algebraic Topology 55M30, 55P15, 57R42 Donald Davis initiated the study of an $n$-dimensional analogue of the Klein bottle. This generalized Klein bottle occurs as a moduli space of planar polygons for a certain choice of side lengths. In this paper, we show that the $n$-dimensional Klein bottle is a real Bott manifold and determine the corresponding Bott matrix. We determine the small cover structure on two other classes of moduli spaces of planar polygons. As an application, we compute the rational Betti numbers of these spaces using a formula, due to Suciu and Trevisan. |
| title | Real Bott manifold structure of $n$-dimensional Klein bottle and its rational Betti numbers |
| topic | Algebraic Topology 55M30, 55P15, 57R42 |
| url | https://arxiv.org/abs/2201.01063 |