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- W1970621844 abstract "In the theory of vector-spaces an ordered, ortho-normal set of r vectors is called an r -frame. Let S n denote the unit sphere in euclidean ( n + 1)-space, where n ≥ 1. By an r -field on S n is meant a continuous function which assigns to each point of S n an r -frame in the tangent space at that point. If q < r we obtain a q -field from an r -field by suppressing the first r – q vectors of each r -frame. Certainly S n admits a 0-field, and does not admit an ( n + 1)-field, since the tangent space is n -dimensional. An n -field on S n is called a parallelism. Notice that an ( n − 1)-field on S n can always be extended to an n -field, since spheres are orientable. The problem is to determine the greatest value of r such that S n admits an r -field." @default.
- W1970621844 created "2016-06-24" @default.
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- W1970621844 date "1957-10-01" @default.
- W1970621844 modified "2023-10-05" @default.
- W1970621844 title "Whitehead products and vector-fields on spheres" @default.
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- W1970621844 doi "https://doi.org/10.1017/s0305004100032928" @default.
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