A category of pseudo-tangles with classifying space Omega S-infinity(infinity) and applications

Abstract

By using Quillen's S-1 S construction, we construct a category 9 with classifying space Q'S, which has a pictorial description by pseudo-tangles. This leads to an elementary interpretation of the generators of the stable stems pi(n)(S) = pi(n)(Omega(infinity)S(infinity)) for n = 0, 1, 2. In addition, we investigate the homotopy fibre, of the inclusion G --> F-P,F-D, where F-P,F-D denotes the free permutative category with duality, and compute the homotopy groups of F-P,F-D for n = 0, 1, 2.