Barycenters of polytope skeleta and counterexamples to the topological Tverberg conjecture, via constraints

DOI10.4171/JEMS/881zbMath1428.52008arXiv1510.07984OpenAlexW2963955427WikidataQ123020113 ScholiaQ123020113MaRDI QIDQ2002836

Florian Frick, Pavle V. M. Blagojević, Günter M. Ziegler

Publication date: 12 July 2019

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.07984

zbMATH Keywords

topological Tverberg theoremconstraint methodgeneralized van Kampen-Flores theoremMabillard-Wagner generalized Whitney trickpolytope skeleta

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Obstruction theory in algebraic topology (55S35) Helly-type theorems and geometric transversal theory (52A35)

Related Items

Eliminating higher-multiplicity intersections. III. Codimension 2, On Reay's relaxed Tverberg conjecture and generalizations of Conway's thrackle conjecture, Tverberg's theorem for cell complexes, ESTIMATING THE SIZE OF THE -COINCIDENCES SET IN REPRESENTATION SPHERES, Colored Tverberg theorem with new constraints on the faces, Beyond the Borsuk–Ulam Theorem: The Topological Tverberg Story, Intersection patterns of finite sets and of convex sets, Regular polygonal partitions of a Tverberg type, Average-value Tverberg partitions via finite Fourier analysis, A Tverberg type theorem for collectively unavoidable complexes, Tverberg’s theorem is 50 years old: A survey, A Tverberg type theorem for matroids, SPLITTING LOOPS AND NECKLACES: VARIANTS OF THE SQUARE PEG PROBLEM, Unavoidable complexes, via an elementary equivariant index theory, The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg, Barycenters of points in polytope skeleta, Helly-type problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Singularities, expanders and topology of maps. II: From combinatorics to topology via algebraic isoperimetry
• Transformation groups
• The colored Tverberg's problem and complexes of injective functions
• On the van Kampen-Flores theorem
• Erratum to ``Notes on the topological Tverberg theorem [Discrete Math. 241, 207-233 (2001)]
• Eliminating higher-multiplicity intersections. III. Codimension 2
• A point in an \(nd\)-polytope is the barycenter of \(n\) points in its \(d\)-faces
• Tverberg plus constraints
• A Generalized van Kampen-Flores Theorem
• On a common generalization of Borsuk's and Radon's theorem
• On a Topological Generalization of a Theorem of Tverberg
• Eliminating Tverberg Points, I. An Analogue of the Whitney Trick
• A Generalization of Radon's Theorem
• Using the Borsuk-Ulam theorem. Lectures on topological methods in combinatorics and geometry. Written in cooperation with Anders Björner and Günter M. Ziegler