Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  techniques from persistent homology are generalized to homotopy groups and to algebraic invariants from knot theory.  define the persistent Alexander module, which can be used to detect knotting in a complex and determine when the knotting changes when vied 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.
['David Letscher']
I am writing a research paper on a idea On persistent homotopy, knotted complexes and the Alexander module
[{"from": "human", "value": "I am writing a research paper on a idea On persistent homotopy, knotted complexes and the Alexander module"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  techniques from persistent homology are generalized to homotopy groups and to algebraic invariants from knot theory.  define the persistent Alexander module, which can be used to detect knotting in a complex and determine when the knotting changes when vied 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."}]