By I. M. James

Professor Peter Hilton is likely one of the top identified mathematicians of his new release. He has released virtually three hundred books and papers on numerous features of topology and algebra. the current quantity is to have fun the party of his 60th birthday. It starts off with a bibliography of his paintings, via reports of his contributions to topology and algebra. those are through 11 study papers excited about a number of themes of present curiosity in algebra and topology. The articles are contributed via a few of the many mathematicians with whom he has labored at one time or one other. This e-book could be of curiosity to either topologists and algebraists, really these interested in homotopy conception.

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**Sample text**

Of Math. 103 (1976), 547-556. [16] H. Samelson, A connection between the Whitehead and the Pontryagin product, Amer. J. of Math. LXXV (1953), 744-752. [17] F. Sigrist and U. Suter, Eine Anwendung der K-Theorie in der Theorie der H-Raume, Comment. Math. Helv. 47 (1) 1972, 36-52. [18] J. Stasheff, Manifolds of the homotopy type of (nonLie) groups, Bull. Amer. Math. Soc. 75 (1969), 998-1000. [19] A. Zabrodsky, The classification of simply connected H-spaces with three cells, II: Math. Scand. 30 (1972), 211-222.

I have already also said that in module theory there is an obvious dual notion, that of p-homotopy. One of the key ideas of Eckmann-Hilton was to translate the dual notions in module theory back into topology. This led to the celebrated Eckmann-Hilton duality. But this really is topology, and no doubt a substantial part of Mislin's essay on Hilton's work in topology [10] will be devoted to a discussion of that Stammbach: The work of Peter Hilton in algebra 36 duality. What is important here, is that this idea also gave rise to a development in category theory.

LXXV (1953), 744-752. [17] F. Sigrist and U. Suter, Eine Anwendung der K-Theorie in der Theorie der H-Raume, Comment. Math. Helv. 47 (1) 1972, 36-52. [18] J. Stasheff, Manifolds of the homotopy type of (nonLie) groups, Bull. Amer. Math. Soc. 75 (1969), 998-1000. [19] A. Zabrodsky, The classification of simply connected H-spaces with three cells, II: Math. Scand. 30 (1972), 211-222. THE WORK OF PETER HILTON IN ALGEBRA Urs Stammbach, ETH Zurich Peter Hilton has published more than 250 articles and books?