2012/06/25 by Ginot, Gregory, Noohi, Behrang · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1206.5603
This paper is a continuations of the project initiated in the book string topology for stacks. We construct string operations on the SO(2)-equivariant homology of the (free) loop space L(X) of an oriented differentiable stack X and show that HSO(2)*+dim(X) -2(L(X)) is a graded Lie algebra. In the particular case where X is a 2-dimensional orbifold we give a Goldman-type description for the string bracket. To prove these results, we develop a machinery of (weak) group actions on topological stacks which should be of independent interest. We explicitly construct the quotient stack of a group acting on a stack and show that it is a topological stack. Then use its homotopy type to define equivariant (co)homology for stacks, transfer maps, and so on.