Hilton's theorem

In algebraic topology, Hilton's theorem, proved by Peter Hilton (1955), states that the loop space of a wedge of spheres is homotopy-equivalent to a product of loop spaces of spheres.

John Milnor (1972) showed more generally that the loop space of the suspension of a wedge of spaces can be written as an infinite product of loop spaces of suspensions of smash products.

References

Hilton, Peter J. (1955), "On the homotopy groups of the union of spheres", Journal of the London Mathematical Society, Second Series, 30 (2): 154–172, doi:10.1112/jlms/s1-30.2.154, ISSN 0024-6107, MR 0068218
Milnor, John Willard (1972) [1956], "On the construction FK", in Adams, John Frank (ed.), Algebraic topology—a student's guide, Cambridge University Press, pp. 118–136, doi:10.1017/CBO9780511662584.011, ISBN 978-0-521-08076-7, MR 0445484

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