Rational spheres and double disk bundles
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866918490009501696 |
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| author | DeVito, Jason Kerin, Martin |
| author_facet | DeVito, Jason Kerin, Martin |
| contents | A manifold $M$ is said to be a double disk bundle if it can be decomposed as a union of two disk bundles glued together by a diffeomorphism of their boundaries. We show that if $M^n$ is a closed simply connected $n$-manifold with $n$ even which is simultaneously a double disk bundle and a rational homology sphere, then $M$ must be homeomorphic to a sphere. In addition, we show that in any dimension, if $M$ is a highly connected rational homology sphere which supports a double disk bundle structure, then its "middle" cohomlogy group must be cyclic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_02150 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Rational spheres and double disk bundles DeVito, Jason Kerin, Martin Differential Geometry 57R15, 57R22, 55R25 A manifold $M$ is said to be a double disk bundle if it can be decomposed as a union of two disk bundles glued together by a diffeomorphism of their boundaries. We show that if $M^n$ is a closed simply connected $n$-manifold with $n$ even which is simultaneously a double disk bundle and a rational homology sphere, then $M$ must be homeomorphic to a sphere. In addition, we show that in any dimension, if $M$ is a highly connected rational homology sphere which supports a double disk bundle structure, then its "middle" cohomlogy group must be cyclic. |
| title | Rational spheres and double disk bundles |
| topic | Differential Geometry 57R15, 57R22, 55R25 |
| url | https://arxiv.org/abs/2105.02150 |