Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A generalized van Kampen-Flores theorem

Author: K. S. Sarkaria
Journal: Proc. Amer. Math. Soc. 111 (1991), 559-565
MSC: Primary 57N10; Secondary 57M05
MathSciNet review: 1004423
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The $ n$-skeleton of a $ (2n + 2)$-simplex does not embed in $ {{\mathbf{R}}^{2n}}$. 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 $ l$ be positive integers such that $ l(p - 1) \leq p(s - 1)$. Then, for any continuous map $ f$ from a $ (ps + p - 2)$-dimensional simplex into $ {{\mathbf{R}}^l}$, there must exist $ p$ points $ \{ {x_1}, \ldots ,{x_p}\} $, lying in pairwise disjoint faces of dimensions $ \leq s - 1$ of this simplex, such that $ f({x_1}) = \cdots = f({x_p})$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57N10, 57M05

Retrieve articles in all journals with MSC: 57N10, 57M05

Additional Information

PII: S 0002-9939(1991)1004423-6
Article copyright: © Copyright 1991 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia