Summary
In[4] we have defined a notion of μ-homotopy in the category of simplicial groups and we have made the conjecture that μ-homotopy is equivalent to loop homotopy. The purpose of this paper is to prove this cojecture.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. Eckmann - P. J. Hilton,Groupes d'homotopie et dualité, I, II, III, C. R. Acad. Sci. Paris (1958), pp. 244, 2555, 2993.
D. M. Kan,On homotopy theory and c.s.s. groups, Ann. of Math.,68 (1958), pp. 38–53.
J. Milnor,The construction FK, Lecture notes, Princeton Univ., Princeton, N.J., 1956.
N. H. Schlomiuk,Principal cofibrations in the category of simplicial groups, Trans. Amer. Math. Soc.,146 (1969), pp. 151–166.
Author information
Authors and Affiliations
Additional information
Entrata in Redazione il 25 febbraio 1972.
This work was done while the author held a Visiting Professorship at the Istituto Matematico, Università di Perugia, under the auspices of the Italian National Research Council.
Rights and permissions
About this article
Cite this article
Schlomiuk, N.H. μ-homotopic maps are loop homotopic. Annali di Matematica 92, 211–215 (1972). https://doi.org/10.1007/BF02417948
Issue Date:
DOI: https://doi.org/10.1007/BF02417948