We show that the deformations of the de Rham cohomology of a closed simply connected KK ahler manifold are governed by the dual of real-valued cohomology of its free loop space. A currently very active eld in Mathematics is the theory of quantum cohomol-ogy, which provides a special kind of deformations of the multiplication structure on the de Rham cohomology of symplectic manifolds. The mathe...

The present paper contains a systematic study of the structure of metric Lie algebras, i.e., finite-dimensional real Lie algebras equipped with a non-degenerate invariant symmetric bilinear form. We show that any metric Lie algebra g without simple ideals has the structure of a so called balanced quadratic extension of an auxiliary Lie algebra l by an orthogonal l-module a in a canonical way. I...

Let A be a symmetric k-algebra over a perfect field k. Külshammer defined for any integer n a mapping ζn on the degree 0 Hochschild cohomology and a mapping κn on the degree 0 Hochschild homology of A as adjoint mappings of the respective p-power mappings with respect to the symmetrizing bilinear form. In an earlier paper it is shown that ζn is invariant under derived equivalences. In the prese...

The complex Mahowald pro-spectrum CP∞ −∞ is not, as might seem at first sight, self-dual; rather, its natural dual is its own double suspension. This assertion makes better sense as a claim about the Tate cohomology spectrum tTS defined by circle actions on framed manifolds. A subtle twist in some duality properties of infinite-dimensional projective space results, which has consequences [via w...

We construct an algebraic commutative ring T -spectrum BO which is stably fibrant and (8, 4)-periodic and such that on SmOp/S the cohomology theory (X, U) 7→ BO(X+/U+) and Schlichting’s hermitian K-theory functor (X, U) 7→ KO [q] 2q−p(X, U) are canonically isomorphic. We use the motivic weak equivalence Z×HGr ∼ −→ KSp relating the infinite quaternionic Grassmannian to symplectic K-theory to equ...

Let A be a local ring with 2 invertible. It is known that the localization of the cohomology ring H∗ ét(A,Z/2) with respect to the class (−1) ∈ H1 ét(A,Z/2) is isomorphic to the ring C(sperA,Z/2) of continuous Z/2-valued functions on the real spectrum of A. Let In(A) denote the powers of the fundamental ideal in the Witt ring of symmetric bilinear forms over A. The starting point of this articl...

As an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of ...

It is well-known (see eg [22]) that the topology of a compact Kähler manifold X is strongly restricted by Hodge theory. In fact, Hodge theory provides two sets of data on the cohomology of a compact Kähler manifold. The first data are the Hodge decompositions on the cohomology spaces H(X,C) (see (1.1) where V = H(X,Q)); they depend only on the complex structure. The second data, known as the Le...