Betti number

mathematics

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June 22, 2026

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Betti numbers are a concept in algebraic topology, a field of mathematics that studies the properties of spaces that are preserved under continuous deformations. Named after the Italian mathematician Enrico Betti, these numbers help characterize the connectivity of a topological space, such as a surface or a higher-dimensional manifold.12

Informally, Betti numbers indicate how many times an object can be "cut" without breaking it into separate pieces. For example, a sphere has a Betti number of 0 because any cut divides it into two parts, while a cylinder has a Betti number of 1 because a cut along its length results in a single, albeit altered, piece. These numbers are topological invariants, meaning they remain the same for spaces that can be continuously deformed into one another.2

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mathematics
Algebraic topology
…a list of numbers, called Betti numbers in honour of the Italian mathematician Enrico Betti, who had taken the first steps of this kind to extend Riemann’s work. It was only in the late 1920s that the German mathematician Emmy Noether suggested how the Betti numbers might be thought of…
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…a list of numbers, called Betti numbers in honour of the Italian mathematician Enrico Betti, who had taken the first steps of this kind to extend Riemann’s work. It was only in the late 1920s that the German mathematician Emmy Noether suggested how the Betti numbers might be thought of…
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homology
…with the introduction of “Betti numbers” in each dimension, referring to the number of independent (suitably defined) objects in that dimension that are not boundaries. Informally, Betti numbers refer to the number of times that an object can be “cut” before splitting into separate pieces; for example, a sphere…
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…with the introduction of “Betti numbers” in each dimension, referring to the number of independent (suitably defined) objects in that dimension that are not boundaries. Informally, Betti numbers refer to the number of times that an object can be “cut” before splitting into separate pieces; for example, a sphere…
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Enrico Betti
…Poincaré to give the name Betti numbers to certain numbers that characterize the connectivity of a manifold (the higher-dimensional analog of a surface).
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…Poincaré to give the name Betti numbers to certain numbers that characterize the connectivity of a manifold (the higher-dimensional analog of a surface).
Read More