-In this paper, we present an assessment of the blocking performance in wavelength routing optical networks with degree-three topologies of minimum diameter. It is analysed a general family of degree-three topologies, of which the chordal ring family is a particular case. Performance results show that all topologies of absolute minimum diameter have exactly the same path blocking probabilities.

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We study almost complex structures with lower bounds on the rank of the Nijenhuis tensor. Namely, we show that they satisfy an h-principle. As a consequence, all parallelizable manifolds and all manifolds of dimension $$2n\ge 10$$ 2 n ≥ 10 (respectively $$\ge 6$$ ≥ 6 ) admit a almost complex structure whose Nijenhuis tensor has maximal rank everywhere (resp. is nowhere trivial). For closed 4-manifolds, the existence of such structures is characterized in terms of topological invariants. Moreover, we show that the Dolbeault cohomology of non-integrable almost complex structures is often infinite dimensional (even on compact manifolds).

We discuss the problem of lifting projective bundles to vector bundles, giving necessary and sufficient conditions for a lift to exist both in the smooth and in the holomorphic categories. These criteria are formulated and proved in the language of topology and complex differential geometry, respectively.We also prove some results about Kähler structures on string six-manifolds. For manifolds without any odd-degree cohomology, one conclusion is that all such Kähler structures are projective and of negative Kodaira dimension.

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