The homology of the little disks operad

Details The homology of the little disks operad The homology of the little disks operad

2006-10-06

arxiv.org/abs/math/0610236v3

Mathematics

Algebraic Topology

Expository paper. 17 pages, 7 figures. Typos corrected, notation cleaned up, and references given in revisions

Scientific paper

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.

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