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The Hochschild cohomology ring of the singular cochain algebra of a space

Katsuhiko Kuribayashi (2011)

Annales de l’institut Fourier

We determine the algebra structure of the Hochschild cohomology of the singular cochain algebra with coefficients in a field on a space whose cohomology is a polynomial algebra. A spectral sequence calculation of the Hochschild cohomology is also described. In particular, when the underlying field is of characteristic two, we determine the associated bigraded Batalin-Vilkovisky algebra structure on the Hochschild cohomology of the singular cochain on a space whose cohomology is an exterior algebra....

The local integration of Leibniz algebras

Simon Covez (2013)

Annales de l’institut Fourier

This article gives a local answer to the coquecigrue problem for Leibniz algebras, that is, the problem of finding a generalization of the (Lie) group structure such that Leibniz algebras are the corresponding tangent algebra structure. Using links between Leibniz algebra cohomology and Lie rack cohomology, we generalize the integration of a Lie algebra into a Lie group by proving that every Leibniz algebra is isomorphic to the tangent Leibniz algebra of a local Lie rack. This article ends with...

The two-square lemma.

Temple H. Fay, Keith A. Hardie, Peter J. Hilton (1989)

Publicacions Matemàtiques

A new proof is given of the connecting homomorphism.

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