10 papers
Equivariant formality and the cohomology of subgroups of right-angled Coxeter groups
Steven Amelotte, Vladimir Gorchakov
We construct models for the classifying spaces of coabelian subgroups of right-angled Coxeter groups as homotopy orbit spaces of real moment-angle complexes, generalizing well-know…
Homotopy types of moment-angle complexes associated to almost linear resolutions
Steven Amelotte, Benjamin Briggs
We show that the Hurewicz image in the homology of a moment-angle complex, when passed through an isomorphism with the Ext-module of the corresponding Stanley-Reisner ideal, contai…
Polyhedral coproducts
Steven Amelotte, William Hornslien, Lewis Stanton
Dualising the construction of a polyhedral product, we introduce the notion of a polyhedral coproduct as a certain homotopy limit over the face poset of a simplicial complex. We be…
Suspension splittings of 5-dimensional Poincaré duality complexes and their applications
Steven Amelotte, Tyrone Cutler, Tseleung So
Let be a connected, orientable, 5-dimensional Poincaré duality complex with torsion-free . We show that is homotopy equivalent to a wedge of recognisabl…
Cohomology operations for moment-angle complexes and resolutions of Stanley-Reisner rings
Steven Amelotte, Benjamin Briggs
A fundamental result in toric topology identifies the cohomology ring of the moment-angle complex associated to a simplicial complex with the Koszul homology of…
Product decompositions of moment-angle manifolds and -rigidity
Steven Amelotte, Benjamin Briggs
A simple polytope is called -rigid if its combinatorial type is determined by the cohomology ring of the moment-angle manifold over . We show that any ten…
Infinite families of higher torsion in the homotopy groups of Moore spaces
Steven Amelotte, Frederick R. Cohen, Yuxin Luo
We give a refinement of the stable Snaith splitting of the double loop space of a Moore space and use it to construct infinite -periodic families of elements of order $p^{r+1}…
Connected sums of sphere products and minimally non-Golod complexes
Steven Amelotte
We show that if the moment-angle complex associated to a simplicial complex is homotopy equivalent to a connected sum of sphere products with two spheres in eac…
The fibre of the degree map, Anick spaces and the double suspension
Steven Amelotte
Let denote the homotopy fibre of the degree self map of . For primes , work of Selick shows that admits a nontrivial loop spa…
A homotopy decomposition of the fibre of the squaring map on
Steven Amelotte
We use Richter's -primary proof of Gray's conjecture to give a homotopy decomposition of the fibre of the -space squaring map on the triple loop space of the…