# Free loop spaces and dihedral homology

@article{Ungheretti2016FreeLS, title={Free loop spaces and dihedral homology}, author={Massimiliano Ungheretti}, journal={arXiv: Algebraic Topology}, year={2016} }

We prove an $O(2)$-equivariant version of the Jones isomorphism relating the Borel $O(2)$-equivariant cohomology of the free loop space to the dihedral homology of the cochain algebra. We discuss polynomial forms and a variation of the de Rham isomorphism and use these to do a computation for the 2-sphere.

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