Finitistic Spaces with Orbit Space a Product of Projective Spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2023
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| _version_ | 1866909091094331392 |
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| author | Kumari, Anju Singh, Hemant Kumar |
| author_facet | Kumari, Anju Singh, Hemant Kumar |
| contents | Let G = Z2 act freely on a nitistic space X. If the mod 2 cohomology of X is isomorphic to the real projective space RP^{2n+1} (resp. complex projective space
CP^{2n+1}) then the mod 2 cohomology of orbit spaces of these free actions are RP1 x CPn (resp. RP2 x HPn) [7]. In this paper, we have discussed converse of these results. We have showed that if the mod 2 cohomology of the orbit space X/G is RP1 x CPn (resp. RP2 x HPn) then the mod 2 cohomology of X is RP^{2n+1} or S1 x CPn (resp. CP^{2n+1} or
S2 x HPn). A partial converse of free involutions on the product of projective spaces RPn x RP2m+1 (resp. CPn x CP2m+1) are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_03724 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finitistic Spaces with Orbit Space a Product of Projective Spaces Kumari, Anju Singh, Hemant Kumar Algebraic Topology Primary 55T10, Secondary 57S99 Let G = Z2 act freely on a nitistic space X. If the mod 2 cohomology of X is isomorphic to the real projective space RP^{2n+1} (resp. complex projective space CP^{2n+1}) then the mod 2 cohomology of orbit spaces of these free actions are RP1 x CPn (resp. RP2 x HPn) [7]. In this paper, we have discussed converse of these results. We have showed that if the mod 2 cohomology of the orbit space X/G is RP1 x CPn (resp. RP2 x HPn) then the mod 2 cohomology of X is RP^{2n+1} or S1 x CPn (resp. CP^{2n+1} or S2 x HPn). A partial converse of free involutions on the product of projective spaces RPn x RP2m+1 (resp. CPn x CP2m+1) are also discussed. |
| title | Finitistic Spaces with Orbit Space a Product of Projective Spaces |
| topic | Algebraic Topology Primary 55T10, Secondary 57S99 |
| url | https://arxiv.org/abs/2306.03724 |