Mathematics – Algebraic Topology
Scientific paper
2009-09-18
Advances in Mathematics 225 (2010), 922-976
Mathematics
Algebraic Topology
57 pages; typos fixed; some comments added. To appear in Adv. in Mathematics
Scientific paper
10.1016/j.aim.2010.03.011
We study torsors over 2-groups and their morphisms. In particular, we study the first non-abelian cohomology group with values in a 2-group. Butterfly diagrams encode morphisms of 2-groups and we employ them to examine the functorial behavior of non-abelian cohomology under change of coefficients. We re-interpret the first non-abelian cohomology with coefficients in a 2-group in terms of gerbes bound by a crossed module. Our main result is to provide a geometric version of the change of coefficients map by lifting a gerbe along the "fraction" (weak morphism) determined by a butterfly. As a practical byproduct, we show how butterflies can be used to obtain explicit maps at the cocycle level. In addition, we discuss various commutativity conditions on cohomology induced by various degrees of commutativity on the coefficient 2-groups, as well as specific features pertaining to group extensions.
Aldrovandi Ettore
Noohi Behrang
No associations
LandOfFree
Butterflies II: Torsors for 2-group stacks 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 Butterflies II: Torsors for 2-group stacks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Butterflies II: Torsors for 2-group stacks will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-276237