On the loop homology of complex projective spaces

The Loop Homology Algebra of Spheres and Projective Spaces

In [3] Chas and Sullivan defined an intersection product on the homology H∗(LM) of the space of smooth loops in a closed, oriented manifold M . In this paper we will use the homotopy theoretic realization of this product described by the first two authors in [2] to construct a second quadrant spectral sequence of algebras converging to the loop homology multiplicatively, when M is simply connec...

Biquaternions Lie Algebra and Complex-Projective Spaces

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Incidence Homology of Finite Projective Spaces

Let F be the finite field of q elements and let P(n, q) be the projective space of dimension n−1 over F. We construct a family H k,i of combinatorial homology modules associated to P(n, q) over a coefficient field F field of characteristic p0 > 0 co-prime to q. As FGL(n, q) -representations the modules are obtained from the permutation action of GL(n, q) on the subspaces of F. We prove a branch...

0 the Homology of Iterated Loop Spaces

Instanton sheaves on complex projective spaces

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...