Computing All Maps into a Sphere
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10286490" target="_blank" >RIV/00216208:11320/14:10286490 - isvavai.cz</a>
Alternative codes found
RIV/00216224:14310/14:00075900
Result on the web
<a href="http://dx.doi.org/10.1145/2597629" target="_blank" >http://dx.doi.org/10.1145/2597629</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1145/2597629" target="_blank" >10.1145/2597629</a>
Alternative languages
Result language
angličtina
Original language name
Computing All Maps into a Sphere
Original language description
Given topological spaces X, Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X -> Y. We consider a computational version, where X, Y are given as finite simplicial complexes, and the goal is to compute[X, Y], that is, all homotopy classes of such maps. We solve this problem in the stable range, where for some d > 1, we have dim X < 2d - 1 and Y is (d - 1)-connected; in particular, Y can bathed-dimensional sphere S-d. The algorithm combines classical tools and ideas from homotopy theory (obstruction theory, Postnikov systems, and simplicial sets) with algorithmic tools froth effective algebraic topology (locally effective simplicial sets and objects with effective homology). In contrast, [X, Y] is known to be uncomputable for general X, Y, since for X = S-1 it includes a well known undecidable problem: testing triviality of the fundamental group of Y. In follow-up papers, the algorithm is shown to run in polynomial time for d fixed, a
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
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach
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
Journal of the ACM
ISSN
0004-5411
e-ISSN
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Volume of the periodical
61
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
46
Pages from-to
1-46
UT code for WoS article
000337201400003
EID of the result in the Scopus database
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