9 citations · 11 across the 2 of their papers we have counts for
5 papers
Topological Deep Learning
Ephy R. Love, Benjamin Filippenko, Vasileios Maroulas +1
This work introduces the Topological CNN (TCNN), which encompasses several topologically defined convolutional methods. Manifolds with important relationships to the natural image…
The space of sections of a smooth function
Gunnar Carlsson, Benjamin Filippenko
Given a compact manifold with boundary and a submersion whose restriction to the boundary of has isolated critical points with distinct critical value…
Persistent homology of the sum metric
Gunnar Carlsson, Benjamin Filippenko
Given finite metric spaces and , we investigate the persistent homology of the Cartesian product equipped with the sum metric $…
A Polyfold Proof of the Arnold Conjecture
Benjamin Filippenko, Katrin Wehrheim
We give a detailed proof of the homological Arnold conjecture for nondegenerate periodic Hamiltonians on general closed symplectic manifolds via a direct Piunikhin-Salamon-Schw…
Polyfold Regularization of Constrained Moduli Spaces
Benjamin Filippenko
We introduce tame sc-Fredholm sections and slices of sc-Fredholm sections. A slice is a notion of subpolyfold that is compatible with the sc-Fredholm section and has finite locally…