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Betti number
Known as:
Betti numbers
, Poincare polynomial
, Poincaré polynomial
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In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes…
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Related topics
Related topics
20 relations
Circuit rank
Computer science
Connected component (graph theory)
Cycle space
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Papers overview
Semantic Scholar uses AI to extract papers important to this topic.
Highly Cited
2013
Highly Cited
2013
Betti numbers in multidimensional persistent homology are stable functions
A. Cerri
,
B. D. Fabio
,
M. Ferri
,
Patrizio Frosini
,
C. Landi
2013
Corpus ID: 9938133
Multidimensional persistence mostly studies topological features of shapes by analyzing the lower level sets of vector‐valued…
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Highly Cited
2010
Highly Cited
2010
The persistent cosmic web and its filamentary structure II: Illustrations
T. Sousbie
,
C. Pichon
,
H. Kawahara
2010
Corpus ID: 119177902
The recently introduced discrete persistent structure extractor (DisPerSE, Soubie 2010, paper I) is implemented on realistic 3D…
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Highly Cited
2009
Highly Cited
2009
Random Geometric Complexes
Matthew Kahle
Discrete & Computational Geometry
2009
Corpus ID: 2128627
We study the expected topological properties of Čech and Vietoris–Rips complexes built on random points in ℝd. We find higher…
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Highly Cited
2008
Highly Cited
2008
Algebraic Properties of Edge Ideals via Combinatorial Topology
A. Dochtermann
,
Alexander Engström
Electronic Journal of Combinatorics
2008
Corpus ID: 2444465
We apply some basic notions from combinatorial topology to establish various algebraic properties of edge ideals of graphs and…
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Highly Cited
2004
Highly Cited
2004
COMPACT RIEMANNIAN 7-MANIFOLDS WITH HOLONOMY G2. I
D. joyce
2004
Corpus ID: 51829286
The list of possible holonomy groups of Riemannian manifolds given by Berger [3] includes three intriguing special cases, the…
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Highly Cited
2001
Highly Cited
2001
Milnor fibers and higher homotopy groups of arrangements
A. Dimca
,
S. Papadima
2001
Corpus ID: 2632819
We describe a new relation between the topology of hypersurface complements, Milnor fibers and degree of gradient mappings. In…
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Highly Cited
1996
Highly Cited
1996
Computing Betti Numbers via Combinatorial Laplacians
Joel Friedman
Symposium on the Theory of Computing
1996
Corpus ID: 60619
Abstract. We use the Laplacian and power method to compute Betti numbers of simplicial complexes. This has a number of advantages…
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Highly Cited
1994
Highly Cited
1994
The Betti numbers of the moduli space of stable sheaves of rank 2 on ℙ[2]
吉岡 康太
1994
Corpus ID: 123202414
Highly Cited
1991
Highly Cited
1991
A new index for polytopes
M. Bayer
,
A. Klapper
Discrete & Computational Geometry
1991
Corpus ID: 6562290
A new index for convex polytopes is introduced. It is a vector whose length is the dimension of the linear span of the flag…
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Review
1976
Review
1976
Some simple examples of symplectic manifolds
W. Thurston
1976
Corpus ID: 122554687
This is a construction of closed symplectic manifolds with no Kaehler structure. A symplectic manifold is a manifold of dimension…
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