Results 1  10
of
271
Notes On The Topological Tverberg Theorem
, 1998
"... . Following a manuscript of K. S. Sarkaria we give an extensive account of the topological Tverberg Theorem in the case where the number of desired disjoint faces is a prime power. Since all known proofs of the theorem use methods from algebraic topology, the objective of this paper is to explain th ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
the proof to a wider mathematical audience. 1. The problem The problem in question is a generalization of a partitioning problem for points in ddimensional euclidean space. In 1966 Helge Tverberg showed the following (see [14], [15] and [10]): Tverberg Theorem (Version I). Let d 1 and q 2 be two
Tverberg graphs
, 2008
"... The topological Tverberg theorem states that for any prime power q and continuous map from a (d + 1)(q − 1)simplex to R d, there are q disjoint faces Fi of the simplex whose images intersect. It is possible to put conditions on which pairs of vertices of the simplex that are allowed to be in the sa ..."
Abstract
 Add to MetaCart
The topological Tverberg theorem states that for any prime power q and continuous map from a (d + 1)(q − 1)simplex to R d, there are q disjoint faces Fi of the simplex whose images intersect. It is possible to put conditions on which pairs of vertices of the simplex that are allowed
On the Topological Tverberg Theorem
, 2008
"... Helge Tverberg proved in 1966 that for every linear map from the ((d + 1)(q − 1))dimensional simplex ∆ (d+1)(q−1) into R d there is a set of q disjoint faces of this simplex such that their images intersect in a point [Tve66]. It is conjectured that such a set of disjoint faces exists for every con ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
continuous map ∆ (d+1)(q−1) → R d as well, but no complete proof of such a “Topological Tverberg Theorem ” is known yet. Up to now, it has only been proven that the conjecture holds in the case that q is a prime power [Vol96]. A proof of the Topological Tverberg Theorem for arbitrary q is considered as one
Tverbergtype theorems . . .
"... Let S be a ddimensional separoid of (k − 1)(d + 1) + 1 convex sets in some ‘largedimensional ’ Euclidean space IE N. We prove a theorem that can be interpreted as follows: if the separoid S can be mapped with a monomorphism to a ddimensional separoid of points P in general position, then there ex ..."
Abstract
 Add to MetaCart
Let S be a ddimensional separoid of (k − 1)(d + 1) + 1 convex sets in some ‘largedimensional ’ Euclidean space IE N. We prove a theorem that can be interpreted as follows: if the separoid S can be mapped with a monomorphism to a ddimensional separoid of points P in general position
Tverberg partitions and Borsuk–Ulam theorems
 Pacific Jour. of Math
"... An Ndimensional real representation E of a finite group G is said to have the “Borsuk–Ulam Property ” if any continuous Gmap from the (N + 1)fold join of G (an Ncomplex equipped with the diagonal Gaction) to E has a zero. This happens iff the “Van Kampen characteristic class ” of E is nonzero, ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
, so using standard computations one can explicitly characterize representations having the BU property. As an application we obtain the “continuous ” Tverberg theorem for all prime powers q, i.e., that some q disjoint faces of a (q − 1)(d+ 1)dimensional simplex must intersect under any continuous
The Topological Tverberg Theorem and winding numbers
 JOURNAL OF COMBINATORIAL THEORY, SERIES A
, 2005
"... The Topological Tverberg Theorem claims that any continuous map of a (q − 1)(d + 1)simplex to R d identifies points from q disjoint faces. (This has been proved for affine maps, for d ≤ 1, and if q is a prime power, but not yet in general.) The Topological Tverberg Theorem can be restricted to maps ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
The Topological Tverberg Theorem claims that any continuous map of a (q − 1)(d + 1)simplex to R d identifies points from q disjoint faces. (This has been proved for affine maps, for d ≤ 1, and if q is a prime power, but not yet in general.) The Topological Tverberg Theorem can be restricted to maps
Tverberg’s theorem with constraints
 J. Combinatorial Theory, Ser. A
, 2008
"... The topological Tverberg theorem claims that for any continuous map of the (q − 1)(d + 1)simplex σ (d+1)(q−1) to R d there are q disjoint faces of σ (d+1)(q−1) such that their images have a nonempty intersection. This has been proved for affine maps, and if q is a prime power, but not in general. ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
. The proof is based on connectivity results of chessboardtype complexes. Moreover, Tverberg’s theorem with constraints implies new lower bounds for the number of Tverberg partitions. As a consequence, we prove Sierksma’s conjecture for d = 2, and q = 3. 1
On the number of colored Birch and Tverberg
, 2014
"... In 2009, Blagojević, Matschke & Ziegler established the first tight colored Tverberg theorem, but no lower bounds for the number of colored Tverberg partitions. We develop a colored version of our previous results (2008), and we extend our results from the uncolored version: Evenness and nontr ..."
Abstract
 Add to MetaCart
In 2009, Blagojević, Matschke & Ziegler established the first tight colored Tverberg theorem, but no lower bounds for the number of colored Tverberg partitions. We develop a colored version of our previous results (2008), and we extend our results from the uncolored version: Evenness and non
ON A THEOREM OF TVERBERG
"... Let ∆ n denote the ndimensional simplex. Any face of ∆ n is assumed to be closed. The wellknown theorem of Radon (see [6]) can be formulated as follows Theorem (Radon). For any linear map f: ∆n+1 → Rn there exist two disjoint faces σ1, σ2 of ∆n+1 such that f(σ1) ∩ f(σ2) = ∅. ..."
Abstract
 Add to MetaCart
Let ∆ n denote the ndimensional simplex. Any face of ∆ n is assumed to be closed. The wellknown theorem of Radon (see [6]) can be formulated as follows Theorem (Radon). For any linear map f: ∆n+1 → Rn there exist two disjoint faces σ1, σ2 of ∆n+1 such that f(σ1) ∩ f(σ2) = ∅.
Results 1  10
of
271