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added this pointer:
I have taken the liberty of re-writing the Idea-section from scratch.
have also included a graphics meant to indicate the role of cycles and dually of cocycles
have not yet included the kind of graphics that most intros to TDA are showing (essentially a stage in a Vietoris-Rips complex) Maybe later.
I have expanded a little more, now there are two Idea-subsections:
In the one on persistent homology/homotopy (here) I have highlighted that the implication of persistent cycles for actually interpreting data in practice is often unclear (and certainly not provided by the mathematics).
In the next one on persistent cohomotopy (now here) I have made explicit that persistent Cohomotopy provides the answer to a concrete and common question about data sets.
Under “Applications” I have added pointer to today’s
using TDA for the recognition of instantons and confinement in lattice gauge theory. This looks interesting.
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