论文信息 - A generalized van Kampen-Flores theorem

A generalized van Kampen-Flores theorem

The n-skeleton of a (2n + 2)-simplex does not embed in R2n. This well-known result is due (independently) to van Kampen, 1932, and Flores, 1933, who proved the case p = 2 of the following: Theorem. Let p be a prime, and let s and I be positive integers such that l(p 1) < p(s 1). Then, for any continuous map f from a (ps + p 2)dimensional simplex into R1, there must exist p points {x ' . . xp} lying in pairwise disjointfaces of dimensions < s 1 of this simplex, such that f(xl) = * (xp)

K. S. Sarkaria

[1] Karol Borsuk. Drei Sätze über die n-dimensionale euklidische Sphäre , 1933 .

[2] Imre Bárány,et al. On a Topological Generalization of a Theorem of Tverberg , 1981 .

[3] J. Radon. Mengen konvexer Körper, die einen gemeinsamen Punkt enthalten , 1921 .

[4] C. Weber. Plongements de polyèdres dans le domaine métastable , 1967 .

[5] H. Tverberg. A Generalization of Radon's Theorem , 1966 .

[6] A. Dold,et al. Simple proofs of some Borsuk - Ulam results , 1983 .

[7] I. Bárány,et al. On a common generalization of Borsuk's and Radon's theorem , 1979 .

[8] K. S. Sarkaria. Kneser colorings of polyhedra , 1989 .

[9] Karanbir S. Sarkaria,et al. A generalized kneser conjecture , 1990, J. Comb. Theory, Ser. B.

[10] E. R. Kampen. Komplexe in euklidischen Räumen , 1933 .

[11] Wen-tsün Wu,et al. A theory of imbedding immersion , and isotopy of polytopes in a euclidean space , 1965 .