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We study configuration spaces of framed points on compact manifolds. Such configuration spaces admit natural actions of the framed little discs operads, that play an important role in the study of embedding spaces of manifolds and in factorization homology. We construct real combinatorial models for these operadic modules, for compact smooth manifolds without boundary.
It is known that the bimodule derived mapping spaces between two operads have a delooping in terms of the operadic mapping space. We show a relative version of that statement. The result has applications to the spaces of disc embeddings fixed near the boundary and framed disc embeddings.
We study the configuration spaces C(n;p,q) of n labeled hard squares in a p by q rectangle, a generalization of the well-known 15 Puzzle. Our main interest is in the topology of these spaces. Our first result is to describe a cubical cell complex and
The equivariant cohomology of the classical configuration space $F(mathbb{R}^d,n)$ has been been of great interest and has been studied intensively starting with the classical papers by Artin (1925/1947) on the theory of braids, by Fox and Neuwirth (
We define and study a model of winding for non-colliding particles in finite trees. We prove that the asymptotic behavior of this statistic satisfies a central limiting theorem, analogous to similar results on winding of bounded particles in the plan
We give a new description of Rosenthals generalized homotopy fixed point spaces as homotopy limits over the orbit category. This is achieved using a simple categorical model for classifying spaces with respect to families of subgroups.