6 papers
Multiparameter persistence modules in the large scale
Martin Frankland, Donald Stanley
A persistence module with discrete parameters is a diagram of vector spaces indexed by the poset . If we are only interested in the large scale behavior of such a…
Moment angle complexes and duality for tight manifolds
Daisuke Kishimoto, Donald Stanley, Carlos Gabriel Valenzuela Ruiz
For a field and a triangulated compact -orientable manifold, consider the homology of the associated Moment-Angle ccomplex …
A stability theorem for bigraded persistence barcodes
Anthony Bahri, Ivan Limonchenko, Taras Panov +2
We define bigraded persistent homology modules and bigraded barcodes of a finite pseudo-metric space X using the ordinary and double homology of the moment-angle complex associated…
Double homology and wedge-decomposable simplicial complexes
Donald Stanley, Carlos Gabriel Valenzuela Ruiz
We show a wedge-decomposable simplicial complex has associated double homology in bidegrees , .
Weighted polyhedral products and Steenrod's problem
Tseleung So, Donald Stanley, Stephen Theriault
We construct a weighted version of polyhedral products and compute its cohomology in special cases. This is applied to resolve Steenrod's cohomology realization problem in a case r…
Classification of homogeneous functors in manifold calculus
Paul Arnaud Songhafouo Tsopmene, Donald Stanley
For any object A in a simplicial model category M, we construct a topological space à which classifies homogeneous functors whose value on k open balls is equivalent to A. This ex…