---
_id: '8184'
abstract:
- lang: eng
  text: "Denote by ∆N the N-dimensional simplex. A map f : ∆N → Rd is an almost r-embedding
    if fσ1∩. . .∩fσr = ∅ whenever σ1, . . . , σr are pairwise disjoint faces. A counterexample
    to the topological Tverberg conjecture asserts that if r is not a prime power
    and d ≥ 2r + 1, then there is an almost r-embedding ∆(d+1)(r−1) → Rd. This was
    improved by Blagojevi´c–Frick–Ziegler using a simple construction of higher-dimensional
    counterexamples by taking k-fold join power of lower-dimensional ones. We improve
    this further (for d large compared to r): If r is not a prime power and N := (d+
    1)r−r l\r\nd + 2 r + 1 m−2, then there is an almost r-embedding ∆N → Rd. For the
    r-fold van Kampen–Flores conjecture we also produce counterexamples which are
    stronger than previously known. Our proof is based on generalizations of the Mabillard–Wagner
    theorem on construction of almost r-embeddings from equivariant maps, and of the
    Ozaydin theorem on existence of equivariant maps. "
acknowledgement: We would like to thank F. Frick for helpful discussions
article_number: '1908.08731'
article_processing_charge: No
arxiv: 1
author:
- first_name: Sergey
  full_name: Avvakumov, Sergey
  id: 3827DAC8-F248-11E8-B48F-1D18A9856A87
  last_name: Avvakumov
  orcid: 0000-0002-7840-5062
- first_name: R.
  full_name: Karasev, R.
  last_name: Karasev
- first_name: A.
  full_name: Skopenkov, A.
  last_name: Skopenkov
citation:
  ama: Avvakumov S, Karasev R, Skopenkov A. Stronger counterexamples to the topological
    Tverberg conjecture. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/arXiv.1908.08731">10.48550/arXiv.1908.08731</a>
  apa: Avvakumov, S., Karasev, R., &#38; Skopenkov, A. (n.d.). Stronger counterexamples
    to the topological Tverberg conjecture. <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.1908.08731">https://doi.org/10.48550/arXiv.1908.08731</a>
  chicago: Avvakumov, Sergey, R. Karasev, and A. Skopenkov. “Stronger Counterexamples
    to the Topological Tverberg Conjecture.” <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/arXiv.1908.08731">https://doi.org/10.48550/arXiv.1908.08731</a>.
  ieee: S. Avvakumov, R. Karasev, and A. Skopenkov, “Stronger counterexamples to the
    topological Tverberg conjecture,” <i>arXiv</i>. .
  ista: Avvakumov S, Karasev R, Skopenkov A. Stronger counterexamples to the topological
    Tverberg conjecture. arXiv, 1908.08731.
  mla: Avvakumov, Sergey, et al. “Stronger Counterexamples to the Topological Tverberg
    Conjecture.” <i>ArXiv</i>, 1908.08731, doi:<a href="https://doi.org/10.48550/arXiv.1908.08731">10.48550/arXiv.1908.08731</a>.
  short: S. Avvakumov, R. Karasev, A. Skopenkov, ArXiv (n.d.).
date_created: 2020-07-30T10:45:34Z
date_published: 2019-08-23T00:00:00Z
date_updated: 2026-04-08T07:25:54Z
day: '23'
department:
- _id: UlWa
doi: 10.48550/arXiv.1908.08731
external_id:
  arxiv:
  - '1908.08731'
  isi:
  - '000986519600004'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1908.08731
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 26611F5C-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P31312
  name: Algorithms for Embeddings and Homotopy Theory
publication: arXiv
publication_status: draft
related_material:
  record:
  - id: '8156'
    relation: dissertation_contains
    status: public
status: public
title: Stronger counterexamples to the topological Tverberg conjecture
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...