Authors: Vrećica, Siniša
Živaljević, Rade 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Fulton-MacPherson compactification, cyclohedra, and the polygonal pegs problem
Journal: Israel Journal of Mathematics
Volume: 184
Issue: 1
First page: 221
Last page: 249
Issue Date: 1-Aug-2011
Rank: M21
ISSN: 0021-2172
DOI: 10.1007/s11856-011-0066-9
Abstract: 
The cyclohedron Wn, known also as the Bott-Taubes polytope, arises both as the polyhedral realization of the poset of all cyclic bracketings of the word x1x2··· xn and as an essential part of the Fulton-MacPherson compactification of the configuration space of n distinct, labelled points on the circle S1. The "polygonal pegs problem" asks whether every simple, closed curve in the plane or in the higher dimensional space admits an inscribed polygon of a given shape. We develop a new approach to the polygonal pegs problem based on the Fulton-MacPherson (Axelrod-Singer, Kontsevich) compactification of the configuration space of (cyclically) ordered n-element subsets in S1. Among the results obtained by this method are proofs of Grünbaum's conjecture about affine regular hexagons inscribed in smooth Jordan curves and a new proof of the conjecture of Hadwiger about inscribed parallelograms in smooth, simple, closed curves in the 3-space (originally established by Makeev in [Mak]).
Publisher: Springer Link
Project: Supported by Grants 144014 and 144026 of the Serbian Ministry of Science and Technology

Show full item record

SCOPUSTM   
Citations

8
checked on Jan 29, 2023

Page view(s)

13
checked on Jan 30, 2023

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.