Volume 13, issue 3 (2013)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 6, 3145–3787
Issue 5, 2527–3144
Issue 4, 1917–2526
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Some Ramsey-type results on intrinsic linking of $n$–complexes

Christopher Tuffley

Algebraic & Geometric Topology 13 (2013) 1579–1612
Abstract

Define the complete n–complex on N vertices, KNn, to be the n–skeleton of an (N 1)–simplex. We show that embeddings of sufficiently large complete n–complexes in 2n+1 necessarily exhibit complicated linking behaviour, thereby extending known results on embeddings of large complete graphs in 3 (the case n = 1) to higher dimensions. In particular, we prove the existence of links of the following types: r–component links, with the linking pattern of a chain, necklace or keyring; 2–component links with linking number at least λ in absolute value; and 2–component links with linking number a nonzero multiple of a given integer q. For fixed n the number of vertices required for each of our results grows at most polynomially with respect to the parameter r, λ or q.

Keywords
intrinsic linking, $n$–complexes, Ramsey theory
Mathematical Subject Classification 2010
Primary: 57Q45
Secondary: 57M15, 57Q35
References
Publication
Received: 8 February 2012
Revised: 17 January 2013
Accepted: 24 January 2013
Published: 16 May 2013
Authors
Christopher Tuffley
Institute of Fundamental Sciences
Massey University
Private Bag 11222
Palmerston North 4442
New Zealand
http://www.massey.ac.nz/~ctuffley/