Title: Manifold theoretic compactifications of configuration spaces.
Author: Dev P. Sinha
AMS Class: 55R80; 32J05 
LANL ID: math.GT/0306385
Addresses: Departments of Mathematics, University of Oregoni, Eugene, OR 97403
Email: dps@math.uoregon.edu 


Abstract:
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.  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.