The Hochschild cohomology of a Poincaré algebra

Details The Hochschild cohomology of a Poincaré algebra The Hochschild cohomology of a Poincaré algebra

2007-07-27

arxiv.org/abs/0707.4118v1

Mathematics

Algebraic Topology

12 pages

Scientific paper

In this note, we define the notion of a cactus set, and show that its geometric realization is naturally an algebra over Voronov's cactus operad, which is equivalent to the framed 2-dimensional little disks operad $\mathcal{D}_2$. Using this, we show that the Hochschild cohomology of a Poincar\'e algebra A is an algebra over (the chain complexes of) $\mathcal{D}_2$.

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