We study a class of torsion-free sheaves on complex projective spaces which generalize the much studied mathematical instanton bundles. Instanton sheaves can be obtained as cohomologies of linear monads and are shown to be semistable if its rank is not too large, while semistable torsion-free sheaves satisfying certain cohomological conditions are instanton. We also study a few examples of modu...

We compute the K-theory of complex projective spaces. There are three major ingredients: the exact sequence of K-groups, the theory of Chern character and the Bott Periodicity Theorem.

Let X be a space and write LX for its free loop space equipped with the action of the circle group T given by dilation. We compute the equivariant cohomology H(LXhT;Z/p) as a module over H ∗(BT;Z/p) when X = CP for any positive integer r and any prime number p. The computation implies that the associated mod p Serre spectral sequence collapses from the E3-page. MSC: 55N91; 58E05; 55P35; 18G50

We work on the classification of isomorphism classes finitely generated projective modules over C*-algebras $C\left( \mathbb{P}^{n}\left( \mathcal{T}\right) \right) $ and \mathbb{S}_{H}^{2n+1}\right) quantum complex spaces $\mathbb{P}^{n}\left( \mathcal{T} spheres $\mathbb{S}_{H}^{2n+1}$, line bundles $L_{k}$ $, studied by Hajac collaborators. Motivated groupoid approach Curto, Muhly, Renault t...