The canonical delooping machine

Bernard Badzioch, Kuerak Chung, Alexander A Voronov

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We suggest a new delooping machine, which is based on recognizing an n-fold loop space by a collection of operations acting on it, like the traditional delooping machines of James, Stasheff, May, Boardman-Vogt, Segal, and Bousfield. Unlike the traditional delooping machines, which carefully select a nice space of such operations, we consider all natural operations on n-fold loop spaces, resulting in the algebraic theory Map* ({n-ary logical or} Sn, {n-ary logical or} Sn). The advantage of this new approach is that the delooping machine is universal in a certain sense, the proof of the recognition principle is more conceptual, it works the same way for all values of n, and it does not need the test space to be connected.

Original languageEnglish (US)
Pages (from-to)531-540
Number of pages10
JournalJournal of Pure and Applied Algebra
Issue number2
StatePublished - Feb 2007

Bibliographical note

Funding Information:
We thank the referee for a number of useful suggestions. The third author was supported in part by NSF grant DMS-0227974.


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