Corpus ID: 119719038

# 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.

#### References

SHOWING 1-10 OF 22 REFERENCES
Free loop space and the cyclic bar construction
Using the $E_\infty-$structure on singular cochains, we construct a homotopy coherent map from the cyclic bar construction of the differential graded algebra of cochains on a space to a model for theExpand
Cyclic homology and equivariant homology
The purpose of this paper is to explore the relationship between the cyclic homology and cohomology theories of Connes [9-11], see also Loday and Quillen [20], and "IF equivariant homology andExpand
Cochain algebras of mapping spaces and finite group actions
• Mathematics
• 2001
Abstract The purpose of the present article is threefold. First of all, we rebuild the whole theory of cosimplicial models of mapping spaces by using systematically Kan adjunction techniques.Expand
Morse theory, closed geodesics, and the homology of free loop spaces
This is a survey paper on Morse theory and the existence problem for closed geodesics. The free loop space plays a central role, since closed geodesics are critical points of the energy functional.Expand
DIHEDRAL HOMOLOGY AND COHOMOLOGY. BASIC NOTIONS AND CONSTRUCTIONS
• Mathematics
• 1988
The subject of the article is the foundations of the theory of dihedral homology and cohomology, the Hermitian analogue of cyclic homology and Connes-Tsygan cohomology. The article consists of fourExpand
ERGODIC PERTURBATIONS OF DEGENERATE INTEGRABLE HAMILTONIAN SYSTEMS
Hamiltonian systems arbitrarily close in the topology to a given integrable degenerate Hamiltonian system of class which generate an ergodic flow on each manifold of constant energy are constructed.Expand
Crossed simplicial groups and their associated homology
• Mathematics
• 1991
We introduce a notion of crossed simplicial group, which generalizes Connes' notion of the cyclic category. We show that this concept has several equivalent descriptions and give a completeExpand
Lectures on Morse theory, old and new
Morse Theory is a beautiful and natural extension of the minimum principle for a continuous function on a compact space. In these lectures I would like to discuss it in the context of two problems inExpand
Periodic geodesics on compact riemannian manifolds
• Mathematics
• 1969
The interest in periodic geodesies arose at a very early stage of differential geometry, and has grown rapidly since then. It is a basic general problem to estimate the number of distinct periodicExpand
301
• Springer,
• 1998