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Persistence Homology on a grid Distance measure

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#algebraic-topology #simplicial-complex #betti-numbers #topological-data-analysis
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Calculating Betti numbers of torus

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#algebraic-topology #betti-numbers
175
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table Betti numbers for real Grassmannians

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#homology-cohomology #grassmannian #betti-numbers
828
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What are the Betti numbers of a double pinched torus?

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#algebraic-topology #homology-cohomology #betti-numbers
96
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Relationship between Betti numbers $b_i(M;\mathbb{Q})$ and the dimension of rational homotopy $\dim_{\mathbb{Q}}\pi_i(M)\otimes\mathbb{Q}$

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#homotopy-theory #betti-numbers #rational-homotopy-theory
254
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calculate Betti numbers of a specific polynomial variety

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#algebraic-topology #betti-numbers
88
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Top non-zero Betti number of connected manifold of finite type.

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#manifolds #homology-cohomology #betti-numbers
234
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Closed oriented even dimensional manifold with only three non-zero Betti numbers.

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#manifolds #homology-cohomology #projective-space #betti-numbers
271
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Closed oriented manifold with middle Betti is one with odd degree.

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#polynomials #algebraic-topology #manifolds #homology-cohomology #betti-numbers
90
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Betti sum, cup-length, Lusternik-Schnirelmann category, and critical points

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#algebraic-topology #fixed-point-theorems #betti-numbers
353
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The second Betti number of a group

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#manifolds #geometric-topology #betti-numbers
197
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Betti Numbers' inequality and Mayer-Vietoris sequence

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#algebraic-topology #exact-sequence #betti-numbers
878
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Why does the Betti number give the measure of k-dimensional holes?

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#algebraic-topology #simplicial-complex #betti-numbers
260
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How to compute the Second and higher order Betti numbers of a graph?

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#algebraic-topology #algebraic-graph-theory #betti-numbers
80
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Closed hyperbolic manifolds with $b_1 = 1$

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#differential-geometry #hyperbolic-geometry #betti-numbers

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