| Title:
|
Homomorphic images and rationalizations based on the Eilenberg-MacLane spaces (English) |
| Author:
|
Lee, Dae-Woong |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
465-470 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Lie bracket |
| Keyword:
|
tensor algebra |
| Keyword:
|
rationalization |
| Keyword:
|
Steenrod power |
| MSC:
|
55P62 |
| MSC:
|
55Q15 |
| MSC:
|
55S37 |
| idZBL:
|
Zbl 1081.55017 |
| idMR:
|
MR2137152 |
| . |
| Date available:
|
2009-09-24T11:24:31Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127992 |
| . |
| Reference:
|
[1] D. Lee and C. A. McGibbon: The same $n$-type problem for certain suspensions.Preprint. |
| Reference:
|
[2] B. Gray: Homotopy theory, an Introduction to Algebraic Topology.Academic Press, New York, 1975. Zbl 0322.55001, MR 0402714 |
| Reference:
|
[3] C. A. McGibbon: Self maps of projective spaces.Trans. Amer. Math. Soc. 271 (1982), 325–346. Zbl 0491.55014, MR 0648096 |
| Reference:
|
[4] C. A. McGibbon: Phantom maps.In: The Handbook of Algebraic Topology, I. M. James (ed.), North-Holland, New York, 1995, pp. . Zbl 0867.55013, MR 1361910 |
| Reference:
|
[5] K. Morisugi: Projective elements in K-theory and self maps of $\Sigma {\mathbb{C}}P^\infty $.J. Math. Kyoto Univ. 38 (1998), 151–165. MR 1628087, 10.1215/kjm/1250518164 |
| Reference:
|
[6] N. E. Steenrod and D. B. A. Epstein: Cohomology operations. Ann. of Math. Stud., No. 50.Princeton University Press, Princeton, 1962, pp. 139. MR 0145525 |
| Reference:
|
[7] D. Sullivan: The genetics of homotopy theory and the Adams conjecture.Ann. of Math. 100 (1974), 1–79. MR 0442930, 10.2307/1970841 |
| . |
