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Paper detail

Persistent homology of semi-algebraic sets

We give an algorithm with singly exponential complexity for computing the barcodes up to dimension $\ell$ (for any fixed $\ell \geq 0$) of the filtration of a given semi-algebraic set by the sub-level sets of a given polynomial. Our algorithm is the first algorithm for this problem with singly exponential complexity, and generalizes the corresponding results for computing the Betti numbers up to dimension $\ell$ of semi-algebraic sets with no filtration present.

preprint2022arXivOpen access
Saugata BasuNegin Karisani
math.AT
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Saugata BasuNegin Karisani

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