Gróbner bases of oriented grassmann manifolds

Tomohiro Fukaya

doi:10.4310/HHA.2008.v10.n2.a10

Gróbner bases of oriented grassmann manifolds

Tomohiro Fukaya

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

For n = 2^m+1 - 4, m ≥ 2, we determine the cup-length of H*(G̃_n,3; ℤ/2) by finding a Gröbner basis associated with a certain subring, where G̃_n,3 is the oriented Grassmann manifold SO(n + 3)/SO(n) x SO(3). As an application, we provide not only a lower but also an upper bound for the LS-category of G̃ _n,3. We also study the immersion problem of G̃_n,3.

Original language	English
Pages (from-to)	195-209
Number of pages	15
Journal	Homology, Homotopy and Applications
Volume	10
Issue number	2
DOIs	https://doi.org/10.4310/HHA.2008.v10.n2.a10
Publication status	Published - 2008
Externally published	Yes

Keywords

Cup-length
Gröbner bases
Immersion
LS-category

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.4310/HHA.2008.v10.n2.a10

Cite this

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AB - For n = 2m+1 - 4, m ≥ 2, we determine the cup-length of H*(G̃n,3; ℤ/2) by finding a Gröbner basis associated with a certain subring, where G̃n,3 is the oriented Grassmann manifold SO(n + 3)/SO(n) x SO(3). As an application, we provide not only a lower but also an upper bound for the LS-category of G̃ n,3. We also study the immersion problem of G̃n,3.

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KW - Immersion

KW - LS-category

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Gróbner bases of oriented grassmann manifolds

Abstract

Keywords

ASJC Scopus subject areas

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