We will give a condition characterizing spaces X with SNT(X) = {[X]} which generalizes the corresponding result of McGibbon and Moller [8] for rational H-spaces.
@article{bwmeta1.element.doi-10_2478_s11533-009-0005-8,
author = {Jinsong Ni},
title = {A criterion of SNT(X) = {[X]} for hyperformal spaces},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {224-229},
zbl = {1180.55005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0005-8}
}
Jinsong Ni. A criterion of SNT(X) = {[X]} for hyperformal spaces. Open Mathematics, Tome 7 (2009) pp. 224-229. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0005-8/
[1] Duan H., Zhao X., The classification of cohomology endomorphisms of certain flag manifolds, Pacific J. Math., 2000, 192, 93–102 http://dx.doi.org/10.2140/pjm.2000.192.93[Crossref] | Zbl 1017.57015
[2] Felix Y., Halperin S., Thomas J.-C., Rational homotopy theory, Graduate Texts in Mathematics 205, Springer-Verlag, New York, 2001 | Zbl 0961.55002
[3] Glover H.H., Mislin G., On the genus of generalized flag manifolds, Enseign. Math. (2), 1982, 27, 211–219 | Zbl 0498.55004
[4] Gray B.I., Spaces of the same n-type, for all n, Topology, 1966, 5, 241–243 http://dx.doi.org/10.1016/0040-9383(66)90008-5[Crossref]
[5] Hilton P., Mislin G., Roitberg J., Homotopical localization, Proc. London Math. Soc. (3), 1973, 26, 693–706 http://dx.doi.org/10.1112/plms/s3-26.4.693[Crossref] | Zbl 0259.55006
[6] Jinsong N., A-phantom maps and spaces have the same (n,A)-type, PhD thesis, Mathematics Institute, Chinese Academy of Sciences, 1998
[7] Jinsong N., Natural mapping on groups of selfhomotopic equivalence of hyperformal spaces have finiteness, Journal of Suzhou University (natural science edition), 2005, 21 (in Chinese)
[8] McGibbon C.A., Møller J.M., On spaces with the same n-type for all n, Topology, 1992, 31, 177–201 http://dx.doi.org/10.1016/0040-9383(92)90069-T[Crossref] | Zbl 0765.55010
[9] Smith S.B., Rational homotopy of the space of self-maps of complexes with finitely many homotopy groups, Trans. Amer. Math. Soc., 1994, 342, 895–915 http://dx.doi.org/10.2307/2154658[Crossref] | Zbl 0802.55009
[10] Smith S.B., Postnikov sections of formal and hyperformal spaces, Proc. Amer. Math. Soc., 1994, 122, 893–903 http://dx.doi.org/10.2307/2160769[Crossref] | Zbl 0826.55006
[11] Wilkerson C., Classification of spaces of the same n-type for all n, Proc. Amer. Math. Soc., 1976, 60, 279–285 http://dx.doi.org/10.2307/2041158[Crossref]
[12] Wilkerson C., Applications of minimal simplicial groups, Topology, 1976, 15, 111–130 http://dx.doi.org/10.1016/0040-9383(76)90001-X[Crossref]