Hilton's theorem

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

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