Volume 16, issue 2 (2016)

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

Volume 19
Issue 2, 533–1078
Issue 1, 1–532

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
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Other MSP Journals
This article is available for purchase or by subscription. See below.
The rational homology of spaces of long links

Paul Arnaud Songhafouo Tsopméné

Algebraic & Geometric Topology 16 (2016) 757–782

We provide a complete understanding of the rational homology of the space of long links of m strands in d when d 4. First, we construct explicitly a cosimplicial chain complex, L, whose totalization is quasi-isomorphic to the singular chain complex of the space of long links. Next we show, using the fact that the Bousfield–Kan spectral sequence associated to L collapses at the E2 page, that the homology Bousfield–Kan spectral sequence associated to the Munson–Volić cosimplicial model for the space of long links collapses at the E2 page rationally, solving a conjecture of B Munson and I Volić. Our method enables us also to determine the rational homology of high-dimensional analogues of spaces of long links. Our last result states that the radius of convergence of the Poincaré series for the space of long links (modulo immersions) tends to zero as m goes to infinity.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

long links, embeddings calculus, module over operads, spectral sequences
Mathematical Subject Classification 2010
Primary: 57Q45
Secondary: 18D50, 18G40, 55P48
Received: 15 September 2014
Revised: 1 July 2015
Accepted: 11 July 2015
Published: 26 April 2016
Paul Arnaud Songhafouo Tsopméné
Institut de Recherche en Mathématique et Physique
Université catholique de Louvain
Chemin du Cyclotron 2
B-1348 Louvain-la-Neuve