6 papers
Iterated Whitehead products in the homotopy groups of polyhedral products
Taras Panov, Stephen Theriault, Fedor Vylegzhanin
We study structure within the homotopy groups of the Davis-Januszkiewicz space DJ(K) associated with a simplicial complex K. The inclusion of each vertex in K induces a map from th…
A colimit decomposition for the loop homology of polyhedral products
Lewis Stanton, Fedor Vylegzhanin
We show that the loop homology algebras of polyhedral products of the form can be written as a colimit over the flagification of $\mat…
Anick's conjecture for polyhedral products
Lewis Stanton, Fedor Vylegzhanin
We develop a method for studying the pointed loop space of general polyhedral products, showing that many properties are determined by the moment-angle complex. To apply the method…
The commutator subalgebra of the Lie algebra associated with a right-angled Coxeter group
Fedor Vylegzhanin, Yakov Veryovkin
We study the graded Lie algebra associated with the lower central series of a right-angled Coxeter group. We construct a surjective homomorphism from the polynomial ring…
Cartesian subgroups in graph products of groups
Fedor Vylegzhanin
The kernel of the natural projection of a graph product of groups onto their direct product is called the Cartesian subgroup of the graph product. This construction generalises com…
Loop homology of moment-angle complexes in the flag case
Fedor Vylegzhanin
We develop a general homological approach to presentations of connected graded associative algebras, and apply it to the loop homology of moment-angle complexes that correspo…