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The Multiplication Problem for Spheres

Howard Stauffer


Abstract. The multiplication problem for spheres is to determine which spheres in Euclidean space Sn-1 - En permit 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 - E8 where the multiplications are given respectively by the real numbers, complex numbers, quaternions, and Cayley numbers.

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