Fast computation of persistent homology representatives with involuted persistent homology

Persistent homology is typically computed through persistent cohomology. While this generally improves the running time significantly, it does not facilitate extraction of representatives. The mentioned representatives are geometric manifestations corresponding holes and often carry desirable information.We propose a new method using In summary, we first compute cohomology use obtained information to significantly improve direct computations. This algorithm applied Rips filtrations computes much faster than standard methods.