On the dual Stiefel-Whitney classes of some Grassmann manifolds

Korbaš, Július; Novotný, Peter

doi:10.1007/s10474-008-8116-4

Cited by 3 publications

(2 citation statements)

References 9 publications

(10 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In general, however, very little information is available concerning the span of a general real flag manifold. See [43] and [38] for span of RG(n − 2, 1, 1) for special values of n.…”

Section: Case (Ii)mentioning

confidence: 99%

The Vector Field Problem for Homogeneous Spaces

Sankaran

2019

Trends in Mathematics

View full text Add to dashboard Cite

Dedicated to Professor Peter Zvengrowski with admiration and respect.Abstract. Let M be a smooth connected manifold of dimension n ≥ 1. A vector field on M is an association p → v(p) of a tangent vector v(p) ∈ T p M for each p ∈ M which varies continuously with p. In more technical language it is a (continuous) cross-section of the tangent bundle τ (M ). The vector field problem asks: Given M , what is the largest possible number r such that there exist vector fields v 1 , . . . , v r which are everywhere linearly independent, that is, v 1 (x), . . . , v r (x) ∈ T x M are linearly independent for every x ∈ M . The number r is called the span of M , written span(M ). It is clear that 0 ≤ span(M ) ≤ dim(M ). The vector field problem is an important and classical problem in differential topology. In this survey we shall consider the vector field problem focussing mainly on the class of compact homogeneous spaces.2010 Mathematics Subject Classification. 57R25.

show abstract

“…In general, however, very little information is available concerning the span of a general real flag manifold. See [43] and [38] for span of RG(n − 2, 1, 1) for special values of n.…”

Section: Case (Ii)mentioning

confidence: 99%

The Vector Field Problem for Homogeneous Spaces

Sankaran

2019

Trends in Mathematics

View full text Add to dashboard Cite

show abstract

“…Although this description is simple enough, concrete calculations in the cohomology is often very difficult to perform (see for example [8,12]). In this paper we show that having a Gröbner basis for the ideal I j,d,n can be very useful for cup-length calculations (see also [10]).…”

Section: A Gröbner Basis For the Cohomology Algebramentioning

confidence: 99%

On the Z2-cohomology cup-length of some real flag manifolds

Radovanović

2016

Filomat

View full text Add to dashboard Cite

In this paper we discuss two different techniques for calculating the Z2-cohomology cup-length - one based on fiberings and a result of Horanska and Korbas, and the other based on Gr?bner bases. We use these techniques to obtain Z2-cohomology cup-length or bounds for the Z2-cohomology cup-length of some of the real flag manifolds F(1,...,1,2...,2,n). [Projekat Ministarstva nauke Republike Srbije, br. 174008]

show abstract