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GROEBNER BASES AND NONEMBEDDINGS OF SOME FLAG MANIFOLDS

Part of: Computational aspects and applications Differential topology

Published online by Cambridge University Press:  31 March 2014

ZORAN Z. PETROVIĆ  and
BRANISLAV I. PRVULOVIĆ
ZORAN Z. PETROVIĆ*
Affiliation:
University of Belgrade, Faculty of Mathematics, Studentski trg 16, Belgrade, Serbia email zoranp@matf.bg.ac.rs
BRANISLAV I. PRVULOVIĆ
Affiliation:
University of Belgrade, Faculty of Mathematics, Studentski trg 16, Belgrade, Serbia email bane@matf.bg.ac.rs
*
✉zoranp@matf.bg.ac.rs
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Abstract

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Groebner bases for the ideals determining mod $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}2$ cohomology of the real flag manifolds $F(1,1,n)$ and $F(1,2,n)$ are obtained. These are used to compute appropriate Stiefel–Whitney classes in order to establish some new nonembedding and nonimmersion results for the manifolds $F(1,2,n)$.

Keywords

flag manifoldGroebner basisimmersionembeddingcuplength

MSC classification

Secondary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 57R40: Embeddings 57R42: Immersions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 96 , Issue 3 , June 2014 , pp. 338 - 353
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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