The paper defines Wasserstein and Fused Gromov-Wasserstein distances for CW complexes by substituting the Hodge Laplacian into existing graph OT formulas.
Menger’s theorem for topological spaces
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Families of Optimal Transport Kernels for Cell Complexes
The paper defines Wasserstein and Fused Gromov-Wasserstein distances for CW complexes by substituting the Hodge Laplacian into existing graph OT formulas.