Betti number
短语[计] 贝蒂数
词形变化
释义与例句
-
1.
Any of a sequence of numbers, denoted bₙ, which characterise a given topological space K by giving, for each dimension, the number of holes in K of said dimension; (formally) the rank of the nth homology group, Hₙ, of K.
数学Poincaré proved that Betti numbers are invariants and used them to extend Euler's polyhedral formula to higher dimensional spaces.
1979 [W. H. Freeman & Company], Michael Henle, A Combinatorial Introduction to Topology, 1994, Dover, page 163, Prove that, for compact surfaces, the zeroth Betti number is the number of components of the surface, where a component is a connected subset of the surface, such that any larger containing subset is not connected.
2007, Oscar García-Prada, Peter Beier Gothen, Vicente Muñoz, Betti Numbers of the Moduli Space of Rank 3 Parabolic Higgs Bundles, American Mathematical Society, page 7, PROPOSITION 2.1. Fix the rank r. For different choices of degrees and generic weights, the moduli spaces of parabolic Higgs bundles have the same Betti numbers.
词源
A calque of French nombre de Betti, coined in 1892 by Henri Poincaré; named after Italian mathematician Enrico Betti in recognition of an 1871 paper.
来源：wiktionary