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- W4386561421 abstract "Persistent homology, building its foundation on homology theory, has been successfully applied various fields containing computation of topology. Here, we derive and implement persistent homology theory to specefic topological spaces with G-invariant covering, whereby persistence over quotient space can be canonically formed. The implementation is validated by comparing against various transformation homomorphisms. Furthermore, it is proved that implementation over normal covering spaces can preserve persistence barcode diagram if charateristic of coefficient is coprime to |G|. These results shed light on potential application of persistent homology to clusters or crystallography in a view of hierarchy structure induced by symmetry." @default.
- W4386561421 created "2023-09-09" @default.
- W4386561421 creator A5007350605 @default.
- W4386561421 date "2023-09-08" @default.
- W4386561421 modified "2023-10-16" @default.
- W4386561421 title "Persistence on Quotient Spaces with G-invariant Covering for Structural Analysis" @default.
- W4386561421 doi "https://doi.org/10.26434/chemrxiv-2023-6c3lk-v2" @default.
- W4386561421 hasPublicationYear "2023" @default.
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