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@article{1376870,
author = {Vokřínek, Lukáš},
article_location = {New York},
article_number = {1},
doi = {http://dx.doi.org/10.1007/s00454-016-9835-x},
keywords = {Homotopy class; Computation; Higher difference},
language = {eng},
issn = {0179-5376},
journal = {Discrete & Computational Geometry},
title = {Decidability of the Extension Problem for Maps into Odd-Dimensional Spheres},
volume = {57},
year = {2017}
}
TY - JOUR
ID - 1376870
AU - Vokřínek, Lukáš
PY - 2017
TI - Decidability of the Extension Problem for Maps into Odd-Dimensional Spheres
JF - Discrete & Computational Geometry
VL - 57
IS - 1
SP - 1-11
EP - 1-11
PB - Springer
SN - 01795376
KW - Homotopy class
KW - Computation
KW - Higher difference
N2 - In a recent paper (Cadek et al., Discrete Comput Geom 51: 24- 66, 2014), it was shown that the problem of the existence of a continuous map X -> Y extending a given map A -> Y, defined on a subspace A subset of X , is undecidable, even for Y an even-dimensional sphere. In the present paper, we prove that the same problem for Y an odd-dimensional sphere is decidable. More generally, the same holds for any d-connected target space Y whose homotopy groups pi_n(Y) are finite for 2d < n < dim X. We also prove an equivariant version, where all spaces are equipped with free actions of a given finite group G and all maps are supposed to respect these actions. This yields the computability of the Z/2-index of a given space up to an uncertainty of 1.
ER -
VOKŘÍNEK, Lukáš. Decidability of the Extension Problem for Maps into Odd-Dimensional Spheres. \textit{Discrete \&{} Computational Geometry}. New York: Springer, 2017, vol.~57, No~1, p.~1-11. ISSN~0179-5376. Available from: https://dx.doi.org/10.1007/s00454-016-9835-x.
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