Homology, Homotopy and Applications

Gröbner bases of oriented Grassmann manifolds

Tomohiro Fukaya

Abstract

For $n = 2{m+1} - 4, m \geq 2$, we determine the cup-length of $H^*(\tilde{G}_{n,3}; \mathbb{Z}/2)$ by finding a Gröbner basis associated with a certain subring, where $\tilde{G}_{n,3}$ is the oriented Grassmann manifold $SO(n + 3)/SO(n) \times SO(3)$. As an application, we provide not only a lower but also an upper bound for the LS-category of $\tilde{G}_{n,3}$. We also study the immersion problem of $\tilde{G}_{n,3}$.

Article information

Source
Homology Homotopy Appl., Volume 10, Number 2 (2008), 195-209.

Dates
First available in Project Euclid: 1 September 2009