## Homology, Homotopy and Applications

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

### Gröbner bases of oriented Grassmann manifolds

#### 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

**Permanent link to this document**

https://projecteuclid.org/euclid.hha/1251811073

**Mathematical Reviews number (MathSciNet)**

MR2475609

**Zentralblatt MATH identifier**

0895.16020

**Subjects**

Primary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space

Secondary: 57T15: Homology and cohomology of homogeneous spaces of Lie groups 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)

**Keywords**

Cup-length LS-category Gröbner bases immersion

#### Citation

Fukaya, Tomohiro. Gröbner bases of oriented Grassmann manifolds. Homology Homotopy Appl. 10 (2008), no. 2, 195--209. https://projecteuclid.org/euclid.hha/1251811073