Cohomology of deformations

Cohomology and Deformations of Algebraic Structures

Gerstenhaber has recently initiated a theory of deformations of associative algebras [4]. The methods and results of Gerstenhaber's work are strikingly similar to those in the theory of deformations of complex analytic structures on compact manifolds. In this note we shall indicate how some of Gerstenhaber's ideas can be reformulated within a framework designed to exploit this similarity, that ...

p-Adic deformations of arithmetic cohomology

Dolbeault Cohomology and Deformations of Nilmanifolds

In these notes I review some classes of invariant complex structures on nilmanifolds for which the Dolbeault cohomology can be computed by means of invariant forms, in the spirit of Nomizu’s theorem for de Rham cohomology. Moreover, deformations of complex structures are discussed. Small deformations remain in some cases invariant, so that, by Kodaira-Spencer theory, Dolbeault cohomology can be...

Deformations of Symplectic Cohomology and Ade Singularities

Let X be the plumbing of copies of the cotangent bundle of a 2−sphere as prescribed by an ADE Dynkin diagram. We prove that the only exact Lagrangian submanifolds in X are spheres. Our approach involves studying X as an ALE hyperkähler manifold and observing that the symplectic cohomology of X will vanish if we deform the exact symplectic form to a generic non-exact one. We will construct the s...

Cohomology and Deformations in Graded Lie Algebras

Introduction. In an address to the Society in 1962, one of the authors gave an outline of the similarities between the deformations of complex-analytic structures on compact manifolds on one hand, and the deformations of associative algebras on the other. The first theory had been stimulated in 1957 by a paper [7] by NijenhuisFrölicher and extensively developed in a series of papers by KodairaS...