There is no topological Fulton-MacPherson compactification
Alexander Kupers
TL;DR
This paper demonstrates that the Fulton-MacPherson compactification cannot be naturally extended from smooth manifolds to topological manifolds, highlighting limitations in topological generalizations of this geometric construction.
Contribution
It provides a proof that the Fulton-MacPherson compactification does not extend naturally to topological manifolds, using recent work by Chen and Mann.
Findings
Fulton-MacPherson compactification is specific to smooth manifolds.
Extension to topological manifolds is not possible in a natural way.
The result clarifies limitations in topological generalizations of configuration space compactifications.
Abstract
In this note we prove that the Fulton-MacPherson compactification of configuration spaces of smooth manifolds can not be extended to topological manifolds in a natural manner, using recent work of Chen and Mann.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Advanced Operator Algebra Research