On fibrations with flat fibres

Valentin Ovsienko; Serge Tabachnikov

doi:10.1112/blms/bds116

On fibrations with flat fibres

Valentin Ovsienko, Serge Tabachnikov

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

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Abstract

We describe the pairs (p, n) such that n-dimensional affine space is fibred by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of composition of quadratic forms.

Original language	English (US)
Pages (from-to)	625-632
Number of pages	8
Journal	Bulletin of the London Mathematical Society
Volume	45
Issue number	3
DOIs	https://doi.org/10.1112/blms/bds116
State	Published - Jun 2013

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1112/blms/bds116

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title = "On fibrations with flat fibres",

abstract = "We describe the pairs (p, n) such that n-dimensional affine space is fibred by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of composition of quadratic forms.",

author = "Valentin Ovsienko and Serge Tabachnikov",

note = "Funding Information: Valentin Ovsienko was partially supported by the PICS05974 {\textquoteleft}PENTAFRIZ{\textquoteright} of CNRS, and Serge Tabachnikov was partially supported by the Simons Foundation grant No 209361 and by the NSF grant DMS-1105442.",

year = "2013",

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doi = "10.1112/blms/bds116",

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AU - Ovsienko, Valentin

AU - Tabachnikov, Serge

N1 - Funding Information: Valentin Ovsienko was partially supported by the PICS05974 ‘PENTAFRIZ’ of CNRS, and Serge Tabachnikov was partially supported by the Simons Foundation grant No 209361 and by the NSF grant DMS-1105442.

PY - 2013/6

Y1 - 2013/6

N2 - We describe the pairs (p, n) such that n-dimensional affine space is fibred by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of composition of quadratic forms.

AB - We describe the pairs (p, n) such that n-dimensional affine space is fibred by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of composition of quadratic forms.

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On fibrations with flat fibres

Abstract

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