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1	A category of pseudo-tangles with classifying space Ω∞ S∞ and applications / Eine Kategorie aus Pseudo-Verschlingungen mit klassifizierendem Raum Ω∞ S∞ und Anwendungen Blömer, Olaf 08 September 2000 (has links) It is well known that the group completion of the classifying space of the free permutative category is Ω∞ S∞, i.e. stable homotopy of the 0-sphere. Quillen´s S-1S construction can be applied to the free permutative category, which has a pictorial description by pseudo-tangles, and this leads to another pictorial descripted category G which has the classifying space Ω∞ S∞. With help of this model G we can give generators for the homotopy groups of Ω∞ S∞ for i=0,1,2. As a further application, we compute the fundamental group of the free permutative category with duality and show that the association of a duality structure on the categorial level does not lead to a group completion on the level of classifying spaces. stable homotopy of spheres classifying space free permutative category duality group completion tangles 55Q45 18D10 55R35 27 - Mathematik ddc:510