TL;DR
This paper links dihedral homology to the equivariant homology of a twisted orthogonal group action on sphere loop spaces, with applications to the restricted three body problem after Moser regularization.
Contribution
It reveals how dihedral homology explains the twisted group actions in the three body problem context.
Findings
Dihedral homology computes equivariant homology of twisted orthogonal actions.
Application to the restricted three body problem after Moser regularization.
Connection between algebraic topology and celestial mechanics.
Abstract
The equivariant homology of a twisted action of the orthogonal group on the free loop space of spheres was computed by Lodder via dihedral homology. In this note we explain how this twisted action appears in the restricted three body problem after Moser regularization.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Black Holes and Theoretical Physics · Noncommutative and Quantum Gravity Theories