Geodesic
Gröbner bases of oriented Grassmann manifolds
Homology, homotopy, and applications, Tome 10 (2008) no. 2, pp. 195-209.

Voir la notice de l'article provenant de la source International Press of Boston

For $n=2^{m+1}-4$, $m\geq 2$, we determine the cup-length of $H^*(\widetilde{G}_{n,3}; \mathbb{Z}/2)$ by finding a Gröbner basis associated with a certain subring, where $\widetilde{G}_{n,3}$ is the oriented Grassmann manifold $\textit{SO}(n+3)/\textit{SO}(n) \times \textit{SO}(3)$. As an application, we provide not only a lower but also an upper bound for the LS-category of $\widetilde{G}_{n,3}$. We also study the immersion problem of $\widetilde{G}_{n,3}$.
DOI : 10.4310/HHA.2008.v10.n2.a10
Classification : 55M30, 13P10, 57T15
Keywords: cup-length, LS-category, Gröbner bases, immersion 
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     author = {Tomohiro Fukaya},
     title = {Gr\"obner bases of oriented {Grassmann} manifolds},
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     pages = {195--209},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n2.a10/}
}
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Tomohiro Fukaya. Gröbner bases of oriented Grassmann manifolds. Homology, homotopy, and applications, Tome 10 (2008) no. 2, pp. 195-209. doi : 10.4310/HHA.2008.v10.n2.a10. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n2.a10/

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