---
res:
bibo_abstract:
- "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. @eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Sergey
foaf_name: Avvakumov, Sergey
foaf_surname: Avvakumov
foaf_workInfoHomepage: http://www.librecat.org/personId=3827DAC8-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: R.
foaf_name: Karasev, R.
foaf_surname: Karasev
- foaf_Person:
foaf_givenName: A.
foaf_name: Skopenkov, A.
foaf_surname: Skopenkov
dct_date: 2019^xs_gYear
dct_identifier:
- UT:000986519600004
dct_language: eng
dct_publisher: arXiv@
dct_title: Stronger counterexamples to the topological Tverberg conjecture@
...