Decidability of the Extension Problem for Maps into Odd-Dimensional Spheres

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F17%3A00094700" target="_blank" >RIV/00216224:14310/17:00094700 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00454-016-9835-x" target="_blank" >http://dx.doi.org/10.1007/s00454-016-9835-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00454-016-9835-x" target="_blank" >10.1007/s00454-016-9835-x</a>

Result language
angličtina
Original language name
Decidability of the Extension Problem for Maps into Odd-Dimensional Spheres
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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