Title

Linear configurations of complete graphs K4 and K5 in R3, and higher dimensional analogs

Document Type

Article

Publication Date

4-1-2017

Abstract

We investigate the space C(X) of images of linearly embedded finite simplicial complexes in R isomorphic to a given complex X, focusing on two special cases: X is the (n - 2)-skeleton K of an n-simplex, and X is the (n - 2)-skeleton L of an (n + 1)-simplex, so X has codimension 2 in R , in both cases. The main result is that for n > 2, C(X) (for either X = K,L) deformation retracts to a subspace homeomorphic to the double mapping cylinder {equation presented}, where An is the alternating group and Sn the symmetric group. The resulting fundamental group provides an example of a generalization of the braid group, which is the fundamental group of the configuration space of points in the plane. n n

Publication Name

Journal of Knot Theory and its Ramifications

Volume Number

26

Issue Number

5

DOI

10.1142/S0218216517500286

Article

1750028

This document is currently not available here.

Share

COinS