




Two multiplications in infinite braidpermutation group 
ChanSeok Jeong, Yongjin Song 
Pages. 7986 


The braidpermutation group $BP_n$ of rank $n$, which is a special
kind of Artin group, is a group of welded braids. It is also
described as a subgroup of the automorphism group of a free group.
The disjoint union of $BP_n$'s forms a symmetric monoidal category
$mathcal{BP}$ so that the group completion of the classifying
space of $mathcal{BP}$ is an infinite loop space. Since the
abelianization of $BP_n$ equals $mathbb{Z} oplus mathbb{Z}/2$
we can conjecture that
$$BBP^+ simeq S^1 imes BSigma_{infty}^+ imes Y,$$ for some
infinite loop space $Y$. V. Vershinin claimed that he constructed
of a splitting map, though a significant gap has been found. In
order to fill the gap we should verify a certain compatibility of
two distinct multiplications on $BBP^+$. 

1. Introduction
2. The braidpermutation group
3. Infinite loop space and a splitting conjecture


braidpermutation group, classifying space, group completion, infinite loop space. 


20F36, 55R35 





