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Keywords:
stable homotopy class; computation; heap
stable homotopy class; computation; heap
Summary:
An algorithmic computation of the set of unpointed stable homotopy classes of equivariant fibrewise maps was described in a recent paper [4] of the author and his collaborators. In the present paper, we describe a simplification of this computation that uses an abelian heap structure on this set that was observed in another paper [5] of the author. A heap is essentially a group without a choice of its neutral element; in addition, we allow it to be empty.
References:
[1] Čadek, M., Krčál, M., Matoušek, J., Sergeraert, F., Vokřínek, L., Wagner, U.: Computing all maps into a sphere. Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA), 2012, preprint, arXiv:1105.6257, 2011. Extended abstract. MR 3205192
[2] Čadek, M., Krčál, M., Matoušek, J., Vokřínek, L., Wagner, U.: Extendability of continuous maps is undecidable. to appear in Discrete Comput. Geom. DOI: http://dx.doi.org/10.1007/s00454-013-9551-8
[3] Čadek, M., Krčál, M., Matoušek, J., Vokřínek, L., Wagner, U.: Polynomial-time computation of homotopy groups and Postnikov systems in fixed dimension. preprint, arXiv:1211.3093, 2012.
[4] Čadek, M., Krčál, M., Vokřínek, L.: Algorithmic solvability of the lifting-extension problem. preprint, arXiv:1307.6444, 2013.
[5] Vokřínek, L.: Heaps and unpointed stable homotopy theory. preprint, arXiv:1312.1709, 2013.
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