---
_id: '1381'
abstract:
- lang: eng
text: 'Motivated by Tverberg-type problems in topological combinatorics and by classical
results about embeddings (maps without double points), we study the question whether
a finite simplicial complex K can be mapped into double-struck Rd without higher-multiplicity
intersections. We focus on conditions for the existence of almost r-embeddings,
i.e., maps f : K → double-struck Rd such that f(σ1) ∩ ⋯ ∩ f(σr) = ∅ whenever σ1,
..., σr are pairwise disjoint simplices of K. Generalizing the classical Haefliger-Weber
embeddability criterion, we show that a well-known necessary deleted product condition
for the existence of almost r-embeddings is sufficient in a suitable r-metastable
range of dimensions: If rd ≥ (r + 1) dim K + 3, then there exists an almost r-embedding
K → double-struck Rd if and only if there exists an equivariant map (K)Δ r → Sr
Sd(r-1)-1, where (K)Δ r is the deleted r-fold product of K, the target Sd(r-1)-1
is the sphere of dimension d(r - 1) - 1, and Sr is the symmetric group. This significantly
extends one of the main results of our previous paper (which treated the special
case where d = rk and dim K = (r - 1)k for some k ≥ 3), and settles an open question
raised there.'
alternative_title:
- LIPIcs
author:
- first_name: Isaac
full_name: Mabillard, Isaac
id: 32BF9DAA-F248-11E8-B48F-1D18A9856A87
last_name: Mabillard
- first_name: Uli
full_name: Wagner, Uli
id: 36690CA2-F248-11E8-B48F-1D18A9856A87
last_name: Wagner
orcid: 0000-0002-1494-0568
citation:
ama: 'Mabillard I, Wagner U. Eliminating higher-multiplicity intersections, II.
The deleted product criterion in the r-metastable range. In: Vol 51. Schloss Dagstuhl-
Leibniz-Zentrum fur Informatik GmbH; 2016:51.1-51.12. doi:10.4230/LIPIcs.SoCG.2016.51'
apa: 'Mabillard, I., & Wagner, U. (2016). Eliminating higher-multiplicity intersections,
II. The deleted product criterion in the r-metastable range (Vol. 51, p. 51.1-51.12).
Presented at the SoCG: Symposium on Computational Geometry, Medford, MA, USA:
Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH. https://doi.org/10.4230/LIPIcs.SoCG.2016.51'
chicago: Mabillard, Isaac, and Uli Wagner. “Eliminating Higher-Multiplicity Intersections,
II. The Deleted Product Criterion in the r-Metastable Range,” 51:51.1-51.12. Schloss
Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, 2016. https://doi.org/10.4230/LIPIcs.SoCG.2016.51.
ieee: 'I. Mabillard and U. Wagner, “Eliminating higher-multiplicity intersections,
II. The deleted product criterion in the r-metastable range,” presented at the
SoCG: Symposium on Computational Geometry, Medford, MA, USA, 2016, vol. 51, p.
51.1-51.12.'
ista: 'Mabillard I, Wagner U. 2016. Eliminating higher-multiplicity intersections,
II. The deleted product criterion in the r-metastable range. SoCG: Symposium on
Computational Geometry, LIPIcs, vol. 51, 51.1-51.12.'
mla: Mabillard, Isaac, and Uli Wagner. Eliminating Higher-Multiplicity Intersections,
II. The Deleted Product Criterion in the r-Metastable Range. Vol. 51, Schloss
Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, 2016, p. 51.1-51.12, doi:10.4230/LIPIcs.SoCG.2016.51.
short: I. Mabillard, U. Wagner, in:, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik
GmbH, 2016, p. 51.1-51.12.
conference:
end_date: 2016-06-17
location: Medford, MA, USA
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2016-06-14
date_created: 2018-12-11T11:51:41Z
date_published: 2016-06-01T00:00:00Z
date_updated: 2021-01-12T06:50:17Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.4230/LIPIcs.SoCG.2016.51
file:
- access_level: open_access
checksum: 92c0c3735fe908f8ded6e484005cb3b1
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:10:06Z
date_updated: 2020-07-14T12:44:47Z
file_id: '4791'
file_name: IST-2016-621-v1+1_LIPIcs-SoCG-2016-51.pdf
file_size: 622969
relation: main_file
file_date_updated: 2020-07-14T12:44:47Z
has_accepted_license: '1'
intvolume: ' 51'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '06'
oa: 1
oa_version: Published Version
page: 51.1 - 51.12
project:
- _id: 25FA3206-B435-11E9-9278-68D0E5697425
grant_number: PP00P2_138948
name: 'Embeddings in Higher Dimensions: Algorithms and Combinatorics'
publication_status: published
publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH
publist_id: '5830'
pubrep_id: '621'
quality_controlled: '1'
scopus_import: 1
status: public
title: Eliminating higher-multiplicity intersections, II. The deleted product criterion
in the r-metastable range
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 51
year: '2016'
...