Geometry-Induced Hodge Stars on Rips and Dowker--Rips Complexes

Jiahui Chen, Sebastian Wilcox

The Vietoris--Rips complex ${\mathrm{VR}}_{\epsilon }(X)$, the Dowker complex ${\mathrm{D}}_R(X,Y)$, and its flagified Dowker--Rips variant ${\mathrm{DR}}_R(X,Y)=\mathrm{F}({\mathrm{D}}_R(X,Y))$ are…