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Regular version of the site

Article

Iterated higher Whitehead products in topology of moment-angle complexes

Siberian Mathematical Journal. 2019. Vol. 60. No. 2. P. 185-196.

We give an example of a simplicial complex whose corresponding moment-angle complex is homotopy equivalent to a wedge of spheres, but there is a sphere that cannot be realized by any linear combination of iterated higher Whitehead products. Using two explicitly defined operations on simplicial complexes, we prove that there exists a simplicial complex that realizes any given iterated higher Whitehead product. Also we describe the smallest simplicial complex that realizes an iterated product with only two pairs of nested brackets.