9 papers
Homotopy rigidity for quasitoric manifolds over a product of simplices
Xin Fu, Tseleung So, Jongbaek Song +1
We consider a variation of the Cohomological Rigidity Problem: whether two quasitoric manifolds whose cohomology rings are isomorphic are homotopy equivalent. We show that if two q…
Local Inertness of Poincaré duality complexes
Samik Basu, Sebastian Chenery, Ruizhi Huang +2
We prove that, under certain homological conditions, the attaching map of the top cell of a Poincaré duality complex is inert when localised away from a finite set of primes. This…
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…
Moment-angle manifolds associated to neighbourly triangulations of spheres
Amaranta Membrillo Solis, Stephen Theriault
We show that a moment-angle manifold associated to a neighbourly triangulation of an odd dimensional sphere is homotopy equivalent to a connected sum of products of two spheres, re…
Pullbacks of Sphere Fibrations over Connected Sums
Sebastian Chenery, Stephen Theriault
We prove conditions under which the total space of the pullback of a sphere fibration over a connected sum is homotopy equivalent to a connected sum with a gyration. Existing resul…
Realizing orders in rational sphere product algebras with three generators
Tseleung So, Donald Stanley, Stephen Theriault +1
The realization problem asks which algebras can be realized as the cohomology of spaces. We study this problem in the context of the orders in a graded rational exterior algebra on…
Loop spaces of -dimensional Poincaré duality complexes whose -skeleton is a co--space
Lewis Stanton, Stephen Theriault
Under certain hypotheses, we prove a loop space decomposition for simply-connected Poincaré Duality complexes of dimension whose -skeleton is a co--space. This unifie…
Polyhedral products associated to pseudomanifolds
Lewis Stanton, Stephen Theriault
We study the homotopy theory of polyhedral products associated to a combinatorial generalisation of manifolds known as pseudomanifolds. As special cases, we show that loop spaces o…
Homotopy rigidity for quasitoric manifolds over a product of -simplices
Xin Fu, Tseleung So, Jongbaek Song +1
For a fixed integer , we show that two quasitoric manifolds over a product of -simplices are homotopy equivalent after appropriate localization, provided that their int…