On certain co–H spaces related to Moore spaces

Stelzer, Manfred

doi:10.1090/S0002-9947-02-02995-1

On certain co–H spaces related to Moore spaces
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by Manfred Stelzer

Trans. Amer. Math. Soc. 354 (2002), 3085-3093

DOI: https://doi.org/10.1090/S0002-9947-02-02995-1

Published electronically: March 29, 2002

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Abstract:

We show that certain co–$H$ spaces, constructed by Anick and Gray, carry a homotopy co–associative and co–commutative co–$H$ structure.

References

David Anick, Differential algebras in topology, Research Notes in Mathematics, vol. 3, A K Peters, Ltd., Wellesley, MA, 1993. MR 1213682
David Anick and Brayton Gray, Small $H$ spaces related to Moore spaces, Topology 34 (1995), no. 4, 859–881. MR 1362790, DOI 10.1016/0040-9383(95)00001-1
Martin Arkowitz, Co-$H$-spaces, Handbook of algebraic topology, North-Holland, Amsterdam, 1995, pp. 1143–1173. MR 1361908, DOI 10.1016/B978-044481779-2/50024-9
Martin Arkowitz and Marek Golasiński, Co-$H$-structures on Moore spaces of type $(G,2)$, Canad. J. Math. 46 (1994), no. 4, 673–686. MR 1289053, DOI 10.4153/CJM-1994-037-0
Israel Berstein and John R. Harper, Cogroups which are not suspensions, Algebraic topology (Arcata, CA, 1986) Lecture Notes in Math., vol. 1370, Springer, Berlin, 1989, pp. 63–86. MR 1000368, DOI 10.1007/BFb0085219
F. R. Cohen, J. C. Moore, and J. A. Neisendorfer, Torsion in homotopy groups, Ann. of Math. (2) 109 (1979), no. 1, 121–168. MR 519355, DOI 10.2307/1971269
Brayton Gray, $EHP$ spectra and periodicity. I. Geometric constructions, Trans. Amer. Math. Soc. 340 (1993), no. 2, 595–616. MR 1152323, DOI 10.1090/S0002-9947-1993-1152323-X
Brayton Gray, $v_2$ periodic homotopy families, Algebraic topology (Oaxtepec, 1991) Contemp. Math., vol. 146, Amer. Math. Soc., Providence, RI, 1993, pp. 129–141. MR 1224911, DOI 10.1090/conm/146/01219
Tudor Ganea, Cogroups and suspensions, Invent. Math. 9 (1969/70), 185–197. MR 267582, DOI 10.1007/BF01404323
John R. Harper, Co-$H$-maps to spheres, Israel J. Math. 66 (1989), no. 1-3, 223–237. MR 1017163, DOI 10.1007/BF02765894
Joseph A. Neisendorfer, The exponent of a Moore space, Algebraic topology and algebraic $K$-theory (Princeton, N.J., 1983) Ann. of Math. Stud., vol. 113, Princeton Univ. Press, Princeton, NJ, 1987, pp. 35–71. MR 921472
Joseph Neisendorfer, Primary homotopy theory, Mem. Amer. Math. Soc. 25 (1980), no. 232, iv+67. MR 567801, DOI 10.1090/memo/0232
Alexander Zabrodsky, Hopf spaces, North-Holland Mathematics Studies, Vol. 22, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1976. MR 0440542