We present two spaces with rich additional structure
which are homotopy equivalent to the space of configurations in
Euclidean space. The first, a subvariety of a product of spheres, is closely
related to the Fulton-MacPherson compactification. The second, a
realization of a simplicial set, is due to Jeff Smith and has been
applied to combinatorial loop space theory. Along the way we indicate
how these models are each, in very different ways, relevant to the study of knots through the calculus of functors.

Keywords:

Complexity; Knot Theory

Lecture #10695

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