Skew Linear Vector Fields on Spheres

Zvengrowski, Peter

doi:10.1112/jlms/s2-3.4.625

Cited by 7 publications

(12 citation statements)

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“…The interest in projective homotopy classes of Stiefel manifolds arises from a problem concerning vector fields on spheres, studied by Zvengrowski [7]. In particular, he asks the following question: Is every r-field on 5 W_1 homotopic to a skew linear r-field?…”

Section: Introduction Given a Homotopy Class [F]mentioning

confidence: 99%

“…In [7] Zvengrowski shows that for r ^ 5, every r-field is homotopic to a skew-linear r-field. The first part of the proof makes use of a homotopy classification of r-fields on 5 W_1 ; the homotopy classes of r-fields are in one-one correspondence with (n -1)-dimensional homotopy classes of the fibre 7T n _i(F n _i, r ).…”

Section: Introduction Given a Homotopy Class [F]mentioning

confidence: 99%

“…when n = 2, 4, or 8. Most of the arguments are elementary and are given in [7]. The concern of this paper is to handle the two non-trivial cases ^7(^7,3) and ^7(^7,4).…”

Section: Introduction Given a Homotopy Class [F]mentioning

confidence: 99%

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Projective Homotopy Classes of Stiefel Manifolds

Strutt

1972

Can. j. math.

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Given a homotopy class [f] in πn(X), we say that [f] is projective if and only if there is a homotopy commutative factorizationwhere v is the standard double covering. We then denote by the subset of projective homotopy classes in πn(X).The notion of projective homotopy classes was studied in the author's thesis [5], and the projective homotopy classes for spheres in the stable range, up through the 3-stem were calculated in [6].

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Section: Introduction Given a Homotopy Class [F]mentioning

confidence: 99%

Section: Introduction Given a Homotopy Class [F]mentioning

confidence: 99%

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Projective Homotopy Classes of Stiefel Manifolds

Strutt

1972

Can. j. math.

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“…By [5] w4 is projective, but w4 can not be halved. Since 2vm(X) consists of projective classes for odd m and any space X by [7], w15 and to3x can be halved (see [3]) and so are projective.…”

Section: And [G°i]=0mentioning

confidence: 99%

“…To determine the integers « for which <on can be halved is an important problem in homotopy theory. A homotopy class [/] e trm(X) is called projective in [7] iff/is homotopic to g ° n for some map g:Pm->-X where Tr:Sm->-Pm denotes the double covering. We remark that con can be halved iff there exists g : P2n~l^-Sn with [g o 7r] = a>"…”

Section: Introductionmentioning

confidence: 99%