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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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