| Title:
|
Heaps and unpointed stable homotopy theory (English) |
| Author:
|
Vokřínek, Lukáš |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
50 |
| Issue:
|
5 |
| Year:
|
2014 |
| Pages:
|
323-332 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we show how certain “stability phenomena” in unpointed model categories provide the sets of homotopy classes with a canonical structure of an abelian heap, i.e. an abelian group without a choice of a zero. In contrast with the classical situation of stable (pointed) model categories, these sets can be empty. (English) |
| Keyword:
|
stable homotopy |
| Keyword:
|
equivariant |
| Keyword:
|
fibrewise |
| MSC:
|
55P42 |
| MSC:
|
55U35 |
| idZBL:
|
Zbl 06487016 |
| idMR:
|
MR3303781 |
| DOI:
|
10.5817/AM2014-5-323 |
| . |
| Date available:
|
2015-01-07T15:00:23Z |
| Last updated:
|
2016-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144074 |
| . |
| Reference:
|
[1] Bergman, G.M., Hausknecht, A.O.: Cogroups and co-rings in categories of associative rings.Math. Surveys Monogr., vol. 45, American Mathematical Society, Providence, RI, 1996. Zbl 0857.16001, MR 1387111, 10.1090/surv/045 |
| Reference:
|
[2] Čadek, M., Krčál, M., Matoušek, J., Vokřínek, L., Wagner, U.: Extendability of continuous maps is undecidable.Discrete Comput. Geom. 51 (2014), 24–66. 10.1007/s00454-013-9551-8 |
| Reference:
|
[3] Čadek, M., Krčál, M., Vokřínek, L.: Algorithmic solvability of the lifting-extension problem.Preprint, arXiv:1307.6444, 2013. |
| Reference:
|
[4] Goerss, P.G., Jardine, J.F.: Simplicial homotopy theory.Birkhäuser Verlag, 1999. Zbl 0949.55001, MR 1711612 |
| Reference:
|
[5] Hirschhorn, P.S.: Model categories and their localizations.Math. Surveys Monogr., vol. 99, American Mathematical Society, 2003. Zbl 1017.55001, MR 1944041 |
| Reference:
|
[6] Mather, M.: Pullbacks in homotopy theory.Canad. J. Math. 28 (1976), 225–263. MR 0402694, 10.4153/CJM-1976-029-0 |
| Reference:
|
[7] : nLab entry on “heap”, http://ncatlab.org/nlab/show/heap.tp://ncatlab.org/nlab/show/heap. |
| Reference:
|
[8] Stephan, M.: Elmendorfs theorem for cofibrantly generated model categories.Preprint, arXiv:1308.0856, 2013. |
| Reference:
|
[9] Vokřínek, L.: Computing the abelian heap of unpointed stable homotopy classes of maps.Arch. Math. (Brno) 49 (5) (2013), 359–368. MR 3159334, 10.5817/AM2013-5-359 |
| . |
