Moment-angle complexes corresponding to substitution complexes

Moment-angle complexes corresponding to substitution complexes

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Semyon Abramyan, HSE University and Skoltech

Zoom link: https://princeton.zoom.us/j/92116764865

Passcode: 114700

We discuss the question of realisability of iterated higher Whitehead products with a given form of nested bracket by simplicial complexes, using the notion of the moment-angle complex Z_K. For an iterated higher Whitehead product w we describe a simplicial complex \partial\Delta_w that realises w. Furthermore, for a particular form of brackets inside w, we prove that \partial\Delta_w is the smallest complex that realises w. For certain w, we show that Z_K is homotopy equivalent to a wedge of (product of) spheres and each sphere is a lift of an iterated higher Whitehead product. If there is still time left we discuss an example with a nonrealisable sphere in a wedge.

This is joint work with Taras Panov.