Yet another delooping machine

Badzioch, Bernard; Chung, Kuerak; Voronov, Alexander A.

Yet another delooping machine

Authors

Badzioch, Bernard

Chung, Kuerak

Voronov, Alexander A.

Description

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 Stasheff, May, Boardman-Vogt, Segal, and Bousfield. Unlike in 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 (V_. S^n, V_. S^n). 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, works the same way for all values of n, and does not need the test space to be connected.
11 pages, 1 figure