3,529 research outputs found
Tensor products of homotopy Gerstenhaber algebras
On the tensor product of two homotopy Gerstenhaber algebras we construct a
Hirsch algebra structure which extends the canonical dg algebra structure. Our
result applies more generally to tensor products of "level 3 Hirsch algebras"
and also to the Mayer-Vietoris double complex.Comment: 13 pages; new Remark 5.4, minor change
Koszul duality and equivariant cohomology for tori
Let T be a torus. We show that Koszul duality can be used to compute the
equivariant cohomology of topological T-spaces as well as the cohomology of
pull backs of the universal T-bundle. The new features are that no further
assumptions about the spaces are made and that the coefficient ring may be
arbitrary. This gives in particular a Cartan-type model for the equivariant
cohomology of a T-space with arbitrary coefficients. Our method works for
intersection homology as well.Comment: 37 pages; to appear in Int. Math. Res. No
Describing toric varieties and their equivariant cohomology
Topologically, compact toric varieties can be constructed as identification
spaces: they are quotients of the product of a compact torus and the order
complex of the fan. We give a detailed proof of this fact, extend it to the
non-compact case and draw several, mostly cohomological conclusions.
In particular, we show that the equivariant integral cohomology of a toric
variety can be described in terms of piecewise polynomials on the fan if the
ordinary integral cohomology is concentrated in even degrees. This generalizes
a result of Bahri-Franz-Ray to the non-compact case. We also investigate
torsion phenomena in integral cohomology.Comment: 13 pages; minor change
Weights in cohomology and the Eilenberg-Moore spectral sequence
We show that in the category of complex algebraic varieties, the
Eilenberg--Moore spectral sequence can be endowed with a weight filtration.
This implies that it degenerates if all involved spaces have pure cohomology.
As application, we compute the rational cohomology of an algebraic -variety
( being a connected algebraic group) in terms of its equivariant
cohomology provided that is pure. This is the case, for example, if
is smooth and has only finitely many orbits. We work in the category of
mixed sheaves; therefore our results apply equally to (equivariant)
intersection homology.Comment: 17 pages, final version, to appear in Annales de l'Institute Fourie
Freeness of equivariant cohomology and mutants of compactified representations
We survey generalisations of the Chang-Skjelbred Lemma for integral
coefficients. Moreover, we construct examples of manifolds with actions of tori
of rank > 2 whose equivariant cohomology is torsion-free, but not free. This
answers a question of Allday's. The "mutants" we construct are obtained from
compactified representations and involve Hopf bundles in a crucial way.Comment: 11 pages; more details on the smooth structure of the mutants; other,
minor change
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