On persistent homotopy, knotted complexes and the Alexander module
David Letscher · 2012
In this paper techniques from persistent homology are generalized to homotopy groups and to algebraic invariants from knot theory. We define the persistent Alexander module, which can be used to detect knotting in a complex and determine when the knotting changes when viewed from different scales. Algorithms that use the persistent Alexander module are also presented and applied to examples including protein structures. While the basic definition of persistent homotopy is known, this is the first work to use it successfully for computations.