Manifold theoretic compactifications of configuration spaces

Details Manifold theoretic compactifications of configuration spaces Manifold theoretic compactifications of configuration spaces

2003-06-26

arxiv.org/abs/math/0306385v3

Mathematics

Geometric Topology

Scientific paper

We present new definitions for and give a comprehensive treatment of the canonical compactification of configuration spaces due to Fulton-MacPherson and Axelrod-Singer in the setting of smooth manifolds, as well as a simplicial variant of this compactification initiated by Kontsevich. Our constructions are elementary and give simple global coordinates for the compactified configuration space of a general manifold embedded in Euclidean space. We stratify the canonical compactification, identifying the diffeomorphism types of the strata in terms of spaces of configurations in the tangent bundle, and give completely explicit local coordinates around the strata as needed to define a manifold with corners. We analyze the quotient map from the canonical to the simplicial compactification, showing it is a homotopy equivalence. We define projection maps and diagonal maps, which for the simplicial variant satisfy cosimplicial identities.

Affiliated with

Also associated with

No associations

Rating

Manifold theoretic compactifications of configuration spaces 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 Manifold theoretic compactifications of configuration spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Manifold theoretic compactifications of configuration spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-335441