Geodesic
Homology Operations Revisited
Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 700-717

Voir la notice de l'article provenant de la source Cambridge University Press

There are two principal kinds of input data for infinite loop space theory, namely E ∞ spaces à la Boardman-Vogt [3] and May [7] and Γ-spaces à la Segal [14]. May and Thomason [13] introduced a common generalization and used it to prove the equivalence of the output obtained from these two kinds of input.This suggests that any invariants of one kind of input should have analogs for the other. Homology operations are among the most basic invariants of E ∞ spaces, and we here establish the analogous invariants for Γ-spaces. The definition is transparently obvious from the point of view of the common generalization but is at first sight rather surprising and unnatural from the point of view of Γ-spaces alone. Probably for this reason, there is no hint of the possibility of a direct definition of homology operations for Γ-spaces in the literature. 
Fiedorowicz, Z.; May, J. P. Homology Operations Revisited. Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 700-717. doi: 10.4153/CJM-1982-048-9
@article{10_4153_CJM_1982_048_9,
     author = {Fiedorowicz, Z. and May, J. P.},
     title = {Homology {Operations} {Revisited}},
     journal = {Canadian journal of mathematics},
     pages = {700--717},
     year = {1982},
     volume = {34},
     number = {3},
     doi = {10.4153/CJM-1982-048-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1982-048-9/}
}
TY  - JOUR
AU  - Fiedorowicz, Z.
AU  - May, J. P.
TI  - Homology Operations Revisited
JO  - Canadian journal of mathematics
PY  - 1982
SP  - 700
EP  - 717
VL  - 34
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1982-048-9/
DO  - 10.4153/CJM-1982-048-9
ID  - 10_4153_CJM_1982_048_9
ER  - 
%0 Journal Article
%A Fiedorowicz, Z.
%A May, J. P.
%T Homology Operations Revisited
%J Canadian journal of mathematics
%D 1982
%P 700-717
%V 34
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1982-048-9/
%R 10.4153/CJM-1982-048-9
%F 10_4153_CJM_1982_048_9

[1] 1. Adams, J. F., Infinite loop spaces, Annals of Math. Studies 90 (Princeton, 1978. Google Scholar

[2] 2. Araki, S. and Kudo, T., Topology of Hn-spaces and H-squaring operations, Mem. Math. Fac. Sci. Kyusyu Univ. Ser. A. 10 (1956), 85–120. Google Scholar

[3] 3. Boardman, J. M. and Vogt, R. M., Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics 34–7 (Springer, 1973. Google Scholar

[4] 4. Cohen, F. R., Lada, T. J. and May, J. P., The homology of iterated loop spaces, Lecture Notes in Mathematics 533 (Springer, 1976. Google Scholar

[5] 5. Dyer, E. and Lashof, R. K., Homology of iterated loop spaces, Amer. J. Math. 84 (1962), 35–88. Google Scholar

[6] 6. Fiedorowicz, Z. and Priddy, S. B., Homology of classical groups over finite fields and their associated infinite loop spaces, Lecture Notes in Mathematics 647 (Springer, 1978. Google Scholar

[7] 7. May, J. P., The geometry of iterated loop spaces, Lecture Notes in Mathematics 271 (Springer, 1972. Google Scholar

[8] 8. May, J. P., EM spaces, group completions, and permutative categories, London Math. Soc. Lecture Note Series 11 (1974), 61–94. Google Scholar

[9] 9. May, J. P., (with contributions by Ray, N., Quinn, F. and Tørnehave, J.), Ex ring spaces and E ring spectra, Lecture Notes in Mathematics 577 (Springer, 1977. Google Scholar

[10] 10. May, J. P., The spectra associated to permutative categories, Topology 17 (1978), 225–228. Google Scholar

[11] 11. May, J. P., Pairings of categories and spectra, J. Pure and Applied Algebra 19 (1980), 299–346. Google Scholar

[12] 12. May, J. P., Multiplicative infinite loop space theory, J. Pure and Applied Algebra, to appear. Google Scholar

[13] 13. May, J. P. and Thomason, R. W., The uniqueness of infinite loop space machines, Topology 17 (1978), 205–224. Google Scholar

[14] 14. Segal, G., Categories and cohomology theories, Topology 13 (1974), 293–312. Google Scholar

[15] 15. Thomason, R. W., Homotopy colimits in the category of small categories, Math. Proc. Camb. Phil. Soc. 85 (1979), 91–109. Google Scholar

[16] 16. Woolfson, R., Hyper-Y-spaces and hyper spectra, Quart. J. Math. Oxford (2), 30 (1979), 229–255. Google Scholar

Cité par Sources :