Title: Yet another delooping machine
Authors: Bernard Badzioch, Kuerak Chung, and Alexander A. Voronov
Author's e-mail address: voronov@math.umn.edu
Authors' mailing address: School of Mathematics, University of
Minnesota, Minneapolis, MN 55455
Included ps or eps files: mor.eps
AMS classification number: 55P48 (Primary); 18C10 (Secondary)
ArXiv submission number: math.AT/0403098
Abstract: 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.