Classifying theory for simplicial parametrized groups

Details Classifying theory for simplicial parametrized groups Classifying theory for simplicial parametrized groups

2012-03-12

arxiv.org/abs/1203.2461v1

Mathematics

Algebraic Topology

30 pages, uses xy-pic

Scientific paper

In this paper we describe a classifying theory for families of simplicial topological groups. If $B$ is a topological space and $G$ is a simplicial topological group, then we can consider the non-abelian cohomology $H(B,G)$ of $B$ with coefficients in $G$. If $G$ is a topological group, thought of as a constant simplicial group, then the set $H(B,G)$ is the set of isomorphism classes of principal $G$ bundles, or $G$ torsors, on $B$. For more general simplicial groups $G$, the set $H(B,G)$ parametrizes the set of equivalence classes of higher $G$ torsors on $B$. In this paper we consider a more general setting where $G$ is replaced by a simplicial group in the category of spaces over $B$. The main result of the paper is that under suitable conditions on $B$ and $G$ there is an isomorphism between $H(B,G)$ and the set of isomorphism classes of fiberwise principal bundles on $B$, with structure group $|G|$ given by the fiberwise geometric realization of $G$.

Affiliated with

Also associated with

No associations

Rating

Classifying theory for simplicial parametrized groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classifying theory for simplicial parametrized groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classifying theory for simplicial parametrized groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-488208