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S. Avvakumov, R. Karasev. Envy-free division using mapping degree, Mathematika, 67:1 (2020), 36–53. arXiv:1907.11183
Original
1907
Earlier work this paper cites.
S. Avvakumov, S. Kudrya. Vanishing of all equivariant obstructions and the mapping degree. Discr. Comp. Geom., 66:3 (2021) 1202–1216. arXiv:1910.12628
Original
1910
Earlier work this paper cites.
T. Bartsch. Topological methods for variational problems with symmetries, Lecture Notes in Mathematics, 1560, Springer-Verlag, Berlin, 1993
1993
Earlier work this paper cites.
F. Frick and P. Soberón , The topological Tverberg problem beyond prime powers, arXiv:2005.05251
Original
2005
Earlier work this paper cites.
Singularities, expanders and topology of maps. Part 2: From combinatorics to topology via algebraic isoperimetry,
M. Gromov, · 2010
Earlier work this paper cites.
P. V. M. Blagojević, F. Frick, and G. M. Ziegler, Tverberg plus constraints, Bull. Lond. Math. Soc. 46:5 (2014), 953-967, arXiv:1401.0690
Original
2014
Earlier work this paper cites.

Similar

I. Mabillard and U. Wagner. Eliminating Tverberg Points, I. An Analogue of the Whitney Trick, Proc. of the 30th Annual Symp. on Comp. Geom. (SoCG’14), ACM, New York, 2014, pp. 171–180
2014
Cited alongside, same era.
F. Frick , Counterexamples to the topological Tverberg conjecture, Oberwolfach reports, 12:1 (2015), 318–321. arXiv:1502.00947
Original
2015
Cited alongside, same era.
I. Bárány, P. V. M. Blagojević and G. M. Ziegler. Tverberg’s Theorem at 50: Extensions and Counterexamples, Notices of the Amer. Math. Soc., 63:7 (2016), 732–739
2016
Cited alongside, same era.
A.T. Fomenko and D.B. Fuchs. Homotopical Topology, Springer, 2016
2016
Cited alongside, same era.
S. Basu and S. Ghosh. Equivariant maps related to the topological Tverberg conjecture, Homology, Homotopy and Applications 19:1 (2017) 155–170
2017

Then

I. Bárány and P. Soberón, Tverberg’s theorem is 50 years old: a survey, Bull. Amer. Math. Soc. (N.S.) 55:4 (2018), 459–492. arXiv:1712.06119
Original
2018
Later among the works it cites.
* S. Shlosman , Topological Tverberg Theorem: the proofs and the counterexamples, Russian Math. Surveys, 73:2 (2018), 175182. arXiv:1804.03120
Original
2018
Later among the works it cites.
* A. Skopenkov, A user’s guide to the topological Tverberg Conjecture, arXiv:1605.05141v4. Abridged earlier published version: Russian Math. Surveys, 73:2 (2018), 323–353
Original
2018
Later among the works it cites.
P. V. M. Blagojević, F. Frick and G. M. Ziegler, Barycenters of Polytope Skeleta and Counterexamples to the Topological Tverberg Conjecture, via Constraints, J. Eur. Math. Soc., 21:7 (2019) 2107-2116. arXiv:1510.07984
Original
2019
Closest in time.

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2019

Stronger counterexamples to the topological Tverberg conjecture

Avvakumov, S., Karasev, R., Skopenkov, A.

Understand

Denote by $\Delta_M$ the $M$-dimensional simplex.

A map $f\colon \Delta_M\to\mathbb R^d$ is an almost $r$-embedding if $f\sigma_1\cap\ldots\cap f\sigma_r=\emptyset$ whenever $\sigma_1,\ldots,\sigma_r$ are pairwise disjoint faces.
A counterexample to the topological Tverberg conjecture asserts that if $r$ is not a prime power and $d\ge2r+1$, then there is an almost $r$-embedding $\Delta_{(d+1)(r-1)}\to\mathbb R^d$.
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.

Built on

S. Avvakumov, R. Karasev. Envy-free division using mapping degree, Mathematika, 67:1 (2020), 36–53. arXiv:1907.11183
Original
1907
Earlier work this paper cites.
S. Avvakumov, S. Kudrya. Vanishing of all equivariant obstructions and the mapping degree. Discr. Comp. Geom., 66:3 (2021) 1202–1216. arXiv:1910.12628
Original
1910
Earlier work this paper cites.
T. Bartsch. Topological methods for variational problems with symmetries, Lecture Notes in Mathematics, 1560, Springer-Verlag, Berlin, 1993
1993
Earlier work this paper cites.
F. Frick and P. Soberón , The topological Tverberg problem beyond prime powers, arXiv:2005.05251
Original
2005
Earlier work this paper cites.
Singularities, expanders and topology of maps. Part 2: From combinatorics to topology via algebraic isoperimetry,
M. Gromov, · 2010
Earlier work this paper cites.
P. V. M. Blagojević, F. Frick, and G. M. Ziegler, Tverberg plus constraints, Bull. Lond. Math. Soc. 46:5 (2014), 953-967, arXiv:1401.0690
Original
2014
Earlier work this paper cites.

Similar

I. Mabillard and U. Wagner. Eliminating Tverberg Points, I. An Analogue of the Whitney Trick, Proc. of the 30th Annual Symp. on Comp. Geom. (SoCG’14), ACM, New York, 2014, pp. 171–180
2014
Cited alongside, same era.
F. Frick , Counterexamples to the topological Tverberg conjecture, Oberwolfach reports, 12:1 (2015), 318–321. arXiv:1502.00947
Original
2015
Cited alongside, same era.
I. Bárány, P. V. M. Blagojević and G. M. Ziegler. Tverberg’s Theorem at 50: Extensions and Counterexamples, Notices of the Amer. Math. Soc., 63:7 (2016), 732–739
2016
Cited alongside, same era.
A.T. Fomenko and D.B. Fuchs. Homotopical Topology, Springer, 2016
2016
Cited alongside, same era.
S. Basu and S. Ghosh. Equivariant maps related to the topological Tverberg conjecture, Homology, Homotopy and Applications 19:1 (2017) 155–170
2017

Then

I. Bárány and P. Soberón, Tverberg’s theorem is 50 years old: a survey, Bull. Amer. Math. Soc. (N.S.) 55:4 (2018), 459–492. arXiv:1712.06119
Original
2018
Later among the works it cites.
* S. Shlosman , Topological Tverberg Theorem: the proofs and the counterexamples, Russian Math. Surveys, 73:2 (2018), 175182. arXiv:1804.03120
Original
2018
Later among the works it cites.
* A. Skopenkov, A user’s guide to the topological Tverberg Conjecture, arXiv:1605.05141v4. Abridged earlier published version: Russian Math. Surveys, 73:2 (2018), 323–353
Original
2018
Later among the works it cites.
P. V. M. Blagojević, F. Frick and G. M. Ziegler, Barycenters of Polytope Skeleta and Counterexamples to the Topological Tverberg Conjecture, via Constraints, J. Eur. Math. Soc., 21:7 (2019) 2107-2116. arXiv:1510.07984
Original
2019
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Cited alongside, same era.

P. V. M. Blagojević and G. M. Ziegler, Beyond the Borsuk-Ulam theorem: The topological Tverberg story, in: A Journey Through Discrete Mathematics, Eds. M. Loebl, J. Nešetřil, R. Thomas, Springer, 2017, 273–341. arXiv:1605.07321v3

Original

2017

Cited alongside, same era.

F. Frick , Counterexamples to the topological Tverberg conjecture, arXiv:1502.00947v1

Original

Cited in the paper.

Théorie des fonctions numériques simplement périodiques. Part II

E. Lucas

Cited in the paper.

I. Mabillard and U. Wagner. Eliminating Higher-Multiplicity Intersections, I. A Whitney Trick for Tverberg-Type Problems. arXiv:1508.02349

Original

Cited in the paper.

I. Mabillard and U. Wagner. Eliminating Higher-Multiplicity Intersections, II. The Deleted Product Criterion in the r r -Metastable Range. arXiv:1601.00876v2

Original

Cited in the paper.

I. Mabillard and U. Wagner. Eliminating Higher-Multiplicity Intersections, II. The Deleted Product Criterion in the r-Metastable Range, Proceedings of the 32nd Annual Symposium on Computational Geometry (SoCG’16)

Cited in the paper.

M. Özaydin, Equivariant maps for the symmetric group, unpublished, http://minds.wisconsin.edu/handle/1793/63829

Cited in the paper.

S. Avvakumov, I. Mabillard, A. Skopenkov and U. Wagner. Eliminating Higher-Multiplicity Intersections, III. Codimension 2, Israel J. Math. 245 (2021) 501–534. arxiv:1511.03501

Original

2021

Closest in time.