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Search: MSC category 13D03 ( (Co)homology of commutative rings and algebras (e.g., Hochschild, Andre-Quillen, cyclic, dihedral, etc.) )

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1. CJM Online first

Xia, Eugene Z.
The algebraic de Rham cohomology of representation varieties
The $\operatorname{SL}(2,\mathbb C)$-representation varieties of punctured surfaces form natural families parameterized by monodromies at the punctures. In this paper, we compute the loci where these varieties are singular for the cases of one-holed and two-holed tori and the four-holed sphere. We then compute the de Rham cohomologies of these varieties of the one-holed torus and the four-holed sphere when the varieties are smooth via the Grothendieck theorem. Furthermore, we produce the explicit Gauss-Manin connection on the natural family of the smooth $\operatorname{SL}(2,\mathbb C)$-representation varieties of the one-holed torus.

Keywords:surface, algebraic group, representation variety, de Rham cohomology
Categories:14H10, 13D03, 14F40, 14H24, 14Q10, 14R20

2. CJM 2002 (vol 54 pp. 1100)

Wood, Peter J.
The Operator Biprojectivity of the Fourier Algebra
In this paper, we investigate projectivity in the category of operator spaces. In particular, we show that the Fourier algebra of a locally compact group $G$ is operator biprojective if and only if $G$ is discrete.

Keywords:locally compact group, Fourier algebra, operator space, projective
Categories:13D03, 18G25, 43A95, 46L07, 22D99

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