Embeddability in the 3-Sphere Is Decidable

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384869" target="_blank" >RIV/00216208:11320/18:10384869 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1145/3078632" target="_blank" >https://doi.org/10.1145/3078632</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/3078632" target="_blank" >10.1145/3078632</a>

Result language

angličtina

Original language name

Embeddability in the 3-Sphere Is Decidable

Original language description

We show that the following algorithmic problem is decidable: given a 2-dimensional simplicial complex, can it be embedded (topologically, or equivalently, piecewise linearly) in R-3? By a known reduction, it suffices to decide the embeddability of a given triangulated 3-manifold X into the 3-sphere S-3. The main step, which allows us to simplify X and recurse, is in proving that if X can be embedded in S-3, then there is also an embedding in which X has a short meridian, that is, an essential curve in the boundary of X bounding a disk in S-3 X with length bounded by a computable function of the number of tetrahedra of X.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of the ACM

ISSN

0004-5411

e-ISSN

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Volume of the periodical

65

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

49

Pages from-to

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UT code for WoS article

000425685900006

EID of the result in the Scopus database

2-s2.0-85042474311