Betti number

Known as: Betti numbers, Poincare polynomial, Poincaré polynomial 
In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes… (More)
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Papers overview

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2012
2012
Let G be a finitely generated group and G = G0 ⊇ G1 ⊇ G2 ⊇ · · · a descending chain of finite index normal subgroups of G. Given… (More)
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2008
2008
We use stratified Morse theory for a manifold with corners to give a new bound for the sum of the Betti numbers of a fewnomial… (More)
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2005
2005
In this paper we describe the first singly exponential algorithm for computing the first Betti number of a given semi-algebraic… (More)
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2001
2001
We prove an extension of the following result of Lubotzky and Madid on the rational cohomology of a nilpotent group G: If b1… (More)
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2000
2000
The behaviour of graded Betti numbers under exterior and symmetric algebraic shifting is studied. It is shown that the extremal… (More)
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2000
2000
Sums of Betti numbers in arbitrary characteristic Nicholas M. Katz Introduction In [Mil], Milnor gave an explicit upper bound for… (More)
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1999
1999
Our main theorem asserts that for all odd n ≥ 3 and 0 < δ ≤ 1, there exists a small constant, i(n, δ) > 0, such that if a simply… (More)
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Highly Cited
1999
Highly Cited
1999
In this paper, we introduces the notion of bounded Betti numbers, and show that the bounded Betti numbers of a closed Riemannian… (More)
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1994
1994
If M is a closed orientable hyperbolic 3-manifold with first Betti number 2 then the volume of M exceeds 0.34. 
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Review
1977
Review
1977
We consider the problem of the relationship of the genus of a graph to its Betti number. We define the function g(p) which is the… (More)
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