Gray's conjecture

In mathematics, Gray's conjecture is a conjecture made by Brayton Gray in 1984 about maps between loop spaces of spheres.{{cite journal | last1=Gray | first1=Brayton | title=Unstable families related to the image of J | doi=10.1017/S0305004100061971 |mr=743705 | year=1984 | journal=Mathematical Proceedings of the Cambridge Philosophical Society | issn=0305-0041 | volume=96 | issue=1 | pages=95–113| bibcode=1984MPCPS..96...95G }} It was later proved by John Harper.{{cite book | last1=Harper | first1=John R. | title=Algebraic topology (Evanston, IL, 1988) | publisher=American Mathematical Society | location=Providence, Rhode Island | series=Contempemporary Mathematics |mr=1022681 | year=1989 | volume=96 | chapter=A proof of Gray's conjecture | pages=189–195}}