Classifying PL $5$-manifolds up to regular genus seven
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- by Maria Rita Casali and Carlo Gagliardi PDF
- Proc. Amer. Math. Soc. 120 (1994), 275-283 Request permission
Abstract:
In the present paper, we show that the only closed orientable $5$-manifolds of regular genus less or equal than seven are the $5$-sphere ${\mathbb {S}^5}$ and the connected sums of $m$ copies of ${\mathbb {S}^1} \times {\mathbb {S}^4}$, with $m \leqslant 7$. As a consequence, the genus of ${\mathbb {S}^3} \times {\mathbb {S}^2}$ is proved to be eight. This suggests a possible approach to the ($3$-dimensional) Poincaré Conjecture, via the well-known classification of simply connected $5$-manifolds, obtained by Smale and Barden.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 275-283
- MSC: Primary 57Q99
- DOI: https://doi.org/10.1090/S0002-9939-1994-1205484-4
- MathSciNet review: 1205484