The homology of the little disks operad
Algebraic Topology
2010-02-20 v3
Abstract
In this expository paper we give an elementary, hands-on computation of the homology of the little disks operad, showing that the homology of a $d-fold loop space is a Poisson algebra. One aim is to familiarize a greater audience with Euclidean configuration spaces, using tools accessible to second-year graduate students. We also give a brief introduction to the theory of operads. New results include identifying the pairing between homology and cohomology of these spaces as a pairing of graphs and trees, and treating the cooperad structure on cohomology.
Keywords
Cite
@article{arxiv.math/0610236,
title = {The homology of the little disks operad},
author = {Dev Sinha},
journal= {arXiv preprint arXiv:math/0610236},
year = {2010}
}
Comments
Expository paper. 17 pages, 7 figures. Typos corrected, notation cleaned up, and references given in revisions