Homomorphic images and rationalizations based on the Eilenberg-MacLane spaces
Czechoslovak Mathematical Journal (2005)
- Volume: 55, Issue: 2, page 465-470
- ISSN: 0011-4642
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topLee, Dae-Woong. "Homomorphic images and rationalizations based on the Eilenberg-MacLane spaces." Czechoslovak Mathematical Journal 55.2 (2005): 465-470. <http://eudml.org/doc/30959>.
@article{Lee2005,
abstract = {Are there any kinds of self maps on the loop structure whose induced homomorphic images are the Lie brackets in tensor algebra? We will give an answer to this question by defining a self map of $\Omega \Sigma K(\mathbb \{Z\}, 2d)$, and then by computing efficiently some self maps. We also study the topological rationalization properties of the suspension of the Eilenberg-MacLane spaces. These results will be playing a powerful role in the computation of the same $n$-type problems and giving us an information about the rational homotopy equivalence.},
author = {Lee, Dae-Woong},
journal = {Czechoslovak Mathematical Journal},
keywords = {Lie bracket; tensor algebra; rationalization; Steenrod power; Lie bracket; tensor algebra; rationalization; Steenrod power},
language = {eng},
number = {2},
pages = {465-470},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Homomorphic images and rationalizations based on the Eilenberg-MacLane spaces},
url = {http://eudml.org/doc/30959},
volume = {55},
year = {2005},
}
TY - JOUR
AU - Lee, Dae-Woong
TI - Homomorphic images and rationalizations based on the Eilenberg-MacLane spaces
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 2
SP - 465
EP - 470
AB - Are there any kinds of self maps on the loop structure whose induced homomorphic images are the Lie brackets in tensor algebra? We will give an answer to this question by defining a self map of $\Omega \Sigma K(\mathbb {Z}, 2d)$, and then by computing efficiently some self maps. We also study the topological rationalization properties of the suspension of the Eilenberg-MacLane spaces. These results will be playing a powerful role in the computation of the same $n$-type problems and giving us an information about the rational homotopy equivalence.
LA - eng
KW - Lie bracket; tensor algebra; rationalization; Steenrod power; Lie bracket; tensor algebra; rationalization; Steenrod power
UR - http://eudml.org/doc/30959
ER -
References
top- The same -type problem for certain suspensions, Preprint.
- Homotopy theory, an Introduction to Algebraic Topology, Academic Press, New York, 1975. (1975) Zbl0322.55001MR0402714
- Self maps of projective spaces, Trans. Amer. Math. Soc. 271 (1982), 325–346. (1982) Zbl0491.55014MR0648096
- Phantom maps, In: The Handbook of Algebraic Topology, I. M. James (ed.), North-Holland, New York, 1995, pp. . (1995) Zbl0867.55013MR1361910
- 10.1215/kjm/1250518164, J. Math. Kyoto Univ. 38 (1998), 151–165. (1998) MR1628087DOI10.1215/kjm/1250518164
- Cohomology operations. Ann. of Math. Stud., No. 50, Princeton University Press, Princeton, 1962, pp. 139. (1962) MR0145525
- 10.2307/1970841, Ann. of Math. 100 (1974), 1–79. (1974) MR0442930DOI10.2307/1970841
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