On a class of fuzzy Kähler-like manifolds

The paper introduces a new Kähler-like fuzzy manifold K(E-infinity). All the Betti numbers and other topological invariants of this manifold have been determined. In particular it is found that the Euler characteristic is equal to 26 + k = 26.18033989 compared with 24 in the K3 Kähler case. On the other hand, the absolute value of the inverse signature was found to be equal to the Sommerfield electromagnetic fine structure constant lifted to 10 dimensions. This gives the manifold profound physical meaning.