---
_id: '2157'
abstract:
- lang: eng
text: '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 ℝ3? By a known reduction, it suffices to decide the embeddability
of a given triangulated 3-manifold X into the 3-sphere S3. The main step, which
allows us to simplify X and recurse, is in proving that if X can be embedded in
S3, then there is also an embedding in which X has a short meridian, i.e., an
essential curve in the boundary of X bounding a disk in S3 nX with length bounded
by a computable function of the number of tetrahedra of X.'
acknowledgement: ERC Advanced Grant No. 267165; Grant GRADR Eurogiga GIG/11/E023 (SNSF-PP00P2-138948);
Swiss National Science Foundation (SNSF-200020-138230).
author:
- first_name: Jiří
full_name: Matoušek, Jiří
last_name: Matoušek
- first_name: Eric
full_name: Sedgwick, Eric
last_name: Sedgwick
- first_name: Martin
full_name: Tancer, Martin
id: 38AC689C-F248-11E8-B48F-1D18A9856A87
last_name: Tancer
orcid: 0000-0002-1191-6714
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Matoušek J, Sedgwick E, Tancer M, Wagner U. Embeddability in the 3 sphere
is decidable. In: *Proceedings of the Annual Symposium on Computational Geometry*.
ACM; 2014:78-84. doi:10.1145/2582112.2582137'
apa: 'Matoušek, J., Sedgwick, E., Tancer, M., & Wagner, U. (2014). Embeddability
in the 3 sphere is decidable. In *Proceedings of the Annual Symposium on Computational
Geometry* (pp. 78–84). Kyoto, Japan: ACM. https://doi.org/10.1145/2582112.2582137'
chicago: Matoušek, Jiří, Eric Sedgwick, Martin Tancer, and Uli Wagner. “Embeddability
in the 3 Sphere Is Decidable.” In *Proceedings of the Annual Symposium on Computational
Geometry*, 78–84. ACM, 2014. https://doi.org/10.1145/2582112.2582137.
ieee: J. Matoušek, E. Sedgwick, M. Tancer, and U. Wagner, “Embeddability in the
3 sphere is decidable,” in *Proceedings of the Annual Symposium on Computational
Geometry*, Kyoto, Japan, 2014, pp. 78–84.
ista: 'Matoušek J, Sedgwick E, Tancer M, Wagner U. 2014. Embeddability in the 3
sphere is decidable. Proceedings of the Annual Symposium on Computational Geometry.
SoCG: Symposium on Computational Geometry 78–84.'
mla: Matoušek, Jiří, et al. “Embeddability in the 3 Sphere Is Decidable.” *Proceedings
of the Annual Symposium on Computational Geometry*, ACM, 2014, pp. 78–84, doi:10.1145/2582112.2582137.
short: J. Matoušek, E. Sedgwick, M. Tancer, U. Wagner, in:, Proceedings of the Annual
Symposium on Computational Geometry, ACM, 2014, pp. 78–84.
conference:
end_date: 2014-06-11
location: Kyoto, Japan
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2014-06-08
date_created: 2018-12-11T11:56:02Z
date_published: 2014-06-01T00:00:00Z
date_updated: 2020-08-11T10:10:11Z
day: '01'
department:
- _id: UlWa
doi: 10.1145/2582112.2582137
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1402.0815
month: '06'
oa: 1
oa_version: Submitted Version
page: 78 - 84
publication: Proceedings of the Annual Symposium on Computational Geometry
publication_status: published
publisher: ACM
publist_id: '4849'
quality_controlled: '1'
related_material:
record:
- id: '425'
relation: later_version
status: public
scopus_import: 1
status: public
title: Embeddability in the 3 sphere is decidable
type: conference
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
year: '2014'
...