Homology, Homotopy and Applications

Gröbner bases of oriented Grassmann manifolds

Tomohiro Fukaya

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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


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