In this paper, we investigate the existence of free involutions on some Wall manifolds and compute mod 2 cohomology algebra correspondent orbit space.

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...

In this note, we define the notion of a cactus set, and show that its geometric realization has a natural structure as an algebra over Voronov’s cactus operad, which is equivalent to the framed 2-dimensional little disks operad D2. Using this, we show that for a Poincaré algebra A, its Hochschild cohomology is an algebra over the (chain complexes of) D2.