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Ricci curvature and betti numbers

✍ Scribed by Guofang Wei

Publisher: Springer-Verlag
Year: 1997
Tongue: English
Weight: 641 KB
Volume: 7
Category: Article
ISSN: 1050-6926
DOI: 10.1007/bf02921630

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We show that any algebraic computation tree or any fixed-degree algebraic tree for solving the membership question of a compact set S R n must have height greater than 0(log(; i (S)))&cn for each i, where ; i (S) is the ith Betti number. This generalizes a well-known result by Ben-Or who proved this