Xin Cheng

Exact Kernel Transfer to Clique Complexes and the Hardness of Normalized Persistence

For clique complexes $X_1\subseteq X_2$, normalized persistence in degree $d$ is $\operatorname{rank}[H_d(X_1)\to H_d(X_2)]/\dim H_d(X_1)$. Estimating it requires exact endpoint homology and the inclusion-induced map, even with inverse-polynomial endpoint Laplacian gaps. We prove that additive-error $1/24$ estimation i...