### 100th anniversary of birthday of Eduard Čech

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An interesting connection between the chromatic number of a graph $G$ and the connectivity of an associated simplicial complex $N\left(G\right)$, its “neighborhood complex”, was found by Lovász in 1978 (cf. L. Lovász [J. Comb. Theory, Ser. A 25, 319-324 (1978; Zbl 0418.05028)]). In 1986 a generalization to the chromatic number of a $k$-uniform hypergraph $H$, for $k$ an odd prime, using an associated simplicial complex $C\left(H\right)$, was found ([N. Alon, P. Frankl and L. Lovász, Trans. Am. Math. Soc. 298, 359-370 (1986; Zbl 0605.05033)],...

The authors generalize a construction of Connes by defining for an $A$-bundle $E$ over smooth manifold $X$ and a reduced cyclic cohomology class $c$ a sequence of de Rham cohomology classes $c{h}_{c}^{k}\left(E\right)$. Here $A$ is a convenient algebra, defined by the authors, and $E$ is a locally trivial bundle with standard fibre a right finitely generated projective $A$-module and bounded $A$-modules homomorphisms as transition functions.

Summary: Arrays of numbers may be written not only on a line (= ``a vector'') or in the plain (= ``a matrix'') but also on a circle (= ``a circular vector''), on a torus (= ``a toroidal matrix'') etc. In the latter case, the immanent index-rotation ambiguity converts the standard ``scalar'' product into a binary operation with several interesting properties.