The Multiplication Problem for Spheres
Abstract
Abstract. The multiplication problem for spheres is to determine which spheres in Euclidean space Sn-1-" Enpermit a continuous multiplication. This paper presents the topological K-theory proof that it is only possible when n = 1, 2, 4, and 8. These cases correspond to S0-" E1, S1-" E2, S3-" E4, and S7-" E8where the multiplications are given respectively by the real numbers, complex numbers, quaternions, and Cayley numbers.
Ringkasan. Masalah pendarapan bagi bola adalah masalah untuk menentukan bola-bola dalam Ruang Euclid Sn-1-" En membenarkan suatu pendarapan yang kontinu. Tulisan ini menyampaikan bukti teori K topologi bahwa hanya dapat terjadi abila n = 1, 2, 4, dan 8. Kasus ini bersesuaian dengan S0-" E1, S1-" E2, S3-" E4, dan S7-" E8 di mana pendarapan-pendarapan diberikan oleh bilangan-bilangan riil, kompleks, kuaternion, dan bilangan Cayley.
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