Computing the abelian heap of unpointed stable homotopy classes of maps

Lukáš Vokřínek

Archivum Mathematicum (2013)

  • Volume: 049, Issue: 5, page 359-368
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Vokřínek, Lukáš. "Computing the abelian heap of unpointed stable homotopy classes of maps." Archivum Mathematicum 049.5 (2013): 359-368. <http://eudml.org/doc/260792>.

@article{Vokřínek2013,
abstract = {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.},
author = {Vokřínek, Lukáš},
journal = {Archivum Mathematicum},
keywords = {stable homotopy class; computation; heap; stable homotopy class; computation; heap},
language = {eng},
number = {5},
pages = {359-368},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Computing the abelian heap of unpointed stable homotopy classes of maps},
url = {http://eudml.org/doc/260792},
volume = {049},
year = {2013},
}

TY - JOUR
AU - Vokřínek, Lukáš
TI - Computing the abelian heap of unpointed stable homotopy classes of maps
JO - Archivum Mathematicum
PY - 2013
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 049
IS - 5
SP - 359
EP - 368
AB - 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.
LA - eng
KW - stable homotopy class; computation; heap; stable homotopy class; computation; heap
UR - http://eudml.org/doc/260792
ER -

References

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  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. (2012) MR3205192
  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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