Extendability of Continuous Maps Is Undecidable
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10286489" target="_blank" >RIV/00216208:11320/14:10286489 - isvavai.cz</a>
Alternative codes found
RIV/00216224:14310/14:00073472
Result on the web
<a href="http://dx.doi.org/10.1007/s00454-013-9551-8" target="_blank" >http://dx.doi.org/10.1007/s00454-013-9551-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00454-013-9551-8" target="_blank" >10.1007/s00454-013-9551-8</a>
Alternative languages
Result language
angličtina
Original language name
Extendability of Continuous Maps Is Undecidable
Original language description
We consider two basic problems of algebraic topology: the extension problem and the computation of higher homotopy groups, from the point of view of computability and computational complexity. The extension problem is the following: Given topological spaces X and Y, a subspace AaS dagger X, and a (continuous) map f:A -> Y, decide whether f can be extended to a continuous map . All spaces are given as finite simplicial complexes, and the map f is simplicial. Recent positive algorithmic results, proved ina series of companion papers, show that for (k-1)-connected Y, ka parts per thousand yen2, the extension problem is algorithmically solvable if the dimension of X is at most 2k-1, and even in polynomial time when k is fixed. Here we show that the condition cannot be relaxed: for , the extension problem with (k-1)-connected Y becomes undecidable. Moreover, either the target space Y or the pair (X,A) can be fixed in such a way that the problem remains undecidable. Our second result, a str
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BD - Information theory
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete and Computational Geometry
ISSN
0179-5376
e-ISSN
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Volume of the periodical
51
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
43
Pages from-to
24-66
UT code for WoS article
000329619100002
EID of the result in the Scopus database
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