Geodesic
Heaps and unpointed stable homotopy theory
Archivum mathematicum, Tome 50 (2014) no. 5, pp. 323-332 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.5817/AM2014-5-323
Classification : 55P42, 55U35
Keywords: stable homotopy; equivariant; fibrewise 
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Vokřínek, Lukáš. Heaps and unpointed stable homotopy theory. Archivum mathematicum, Tome 50 (2014) no. 5, pp. 323-332. doi: 10.5817/AM2014-5-323

[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. | DOI | MR | Zbl

[2] Čadek, M., Krčál, M., Matoušek, J., Vokřínek, L., Wagner, U.: Extendability of continuous maps is undecidable. Discrete Comput. Geom. 51 (2014), 24–66. | DOI

[3] Čadek, M., Krčál, M., Vokřínek, L.: Algorithmic solvability of the lifting-extension problem. Preprint, arXiv:1307.6444, 2013.

[4] Goerss, P.G., Jardine, J.F.: Simplicial homotopy theory. Birkhäuser Verlag, 1999. | MR | Zbl

[5] Hirschhorn, P.S.: Model categories and their localizations. Math. Surveys Monogr., vol. 99, American Mathematical Society, 2003. | MR | Zbl

[6] Mather, M.: Pullbacks in homotopy theory. Canad. J. Math. 28 (1976), 225–263. | DOI | MR

[7] nLab entry on “heap”, http://ncatlab.org/nlab/show/heap</b> tp://ncatlab.org/nlab/show/heap.

[8] Stephan, M.: Elmendorfs theorem for cofibrantly generated model categories. Preprint, arXiv:1308.0856, 2013.

[9] Vokřínek, L.: Computing the abelian heap of unpointed stable homotopy classes of maps. Arch. Math. (Brno) 49 (5) (2013), 359–368. | DOI | MR

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