Volume 20, issue 3 (2020)

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

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

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
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Relative recognition principle

Renato Vasconcellos Vieira

Algebraic & Geometric Topology 20 (2020) 1431–1486

We prove the recognition principle for relative N–loop pairs of spaces for 3 N . If 3 N < , this states that a pair of spaces homotopy equivalent to CW–complexes (Xc,Xo) is homotopy equivalent to (Y 𝕊N ,HFib(ι)𝕊N1 ) for a functorially determined relative space ι: B Y if and only if (Xc,Xo) is a grouplike 𝒮𝒞¯N–space, where 𝒮𝒞¯N is any cofibrant resolution of the Swiss-cheese relative operad 𝒮𝒞N. The relative recognition principle for relative –loop pairs of spaces states that a pair of spaces (Xc,Xo) homotopy equivalent to CW–complexes is homotopy equivalent to (Y 0,HFib(ι0)) for a functorially determined relative spectrum ι: B Y +1 if and only if (Xc,Xo) is a grouplike –algebra, where is a contractible cofibrant relative operad or equivalently a cofibrant resolution of the terminal relative operad Com of continuous homomorphisms of commutative monoids. These principles are proved as equivalences of homotopy categories.

PDF Access Denied

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:

infinite loop spaces, recognition principle, stable homotopy theory, relative loop spaces, spectra, relative operads, model category theory, operads
Mathematical Subject Classification 2010
Primary: 55P35, 55P48, 55R15
Secondary: 55P42
Received: 26 September 2018
Revised: 21 February 2019
Accepted: 6 March 2019
Published: 27 May 2020
Renato Vasconcellos Vieira
São Paulo