Homological reconstruction and simplification in R <sup>3</sup>
Homological reconstruction and simplification in R <sup>3</sup>
We consider the problem of deciding whether the persistent homology group of a simplicial pair (K,L) can be realized as the homology of some complex H*(X) with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in R3. As a consequence, we …