Volume 23, issue 3 (2019)

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

Volume 25
Issue 6, 2713–3256
Issue 5, 2167–2711
Issue 4, 1631–2166
Issue 3, 1087–1630
Issue 2, 547–1085
Issue 1, 1–546

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
A finite $\mathbb{Q}$–bad space

Sergei O Ivanov and Roman Mikhailov

Geometry & Topology 23 (2019) 1237–1249

We prove that, for a free noncyclic group F, the second homology group H2(F̂, ) is an uncountable –vector space, where F̂ denotes the –completion of F. This solves a problem of A K Bousfield for the case of rational coefficients. As a direct consequence of this result, it follows that a wedge of two or more circles is –bad in the sense of Bousfield–Kan. The same methods as used in the proof of the above result serve to show that H2(F̂, ) is not a divisible group, where F̂ is the integral pronilpotent completion of F.

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:

homology, nilpotent completion, Bousfield–Kan completion, R–good space, R–bad space
Mathematical Subject Classification 2010
Primary: 14F35, 16W60, 55P60
Received: 27 July 2017
Revised: 29 July 2018
Accepted: 29 September 2018
Published: 28 May 2019
Proposed: Mark Behrens
Seconded: Haynes R Miller, Stefan Schwede
Sergei O Ivanov
Laboratory of Modern Algebra and Applications
St. Petersburg State University
Saint Petersburg
Roman Mikhailov
Laboratory of Modern Algebra and Applications
St. Petersburg State University
Saint Petersburg
St. Petersburg Department of Steklov Mathematical Institute
Saint Petersburg