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Interpretation of eigenvalues and eigenvectors of combinatorial Hodge Laplacian in algebraic topology

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#algebraic-topology #hodge-theory #betti-numbers
46
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Universal coefficient theorem for a surface groups

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#homology-cohomology #group-actions #exact-sequence #betti-numbers
43
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second betti number of surface groups

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#homology-cohomology #riemann-surfaces #betti-numbers
84
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What Does It Mean to Say that Betti Numbers Count Holes?

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#algebraic-topology #homology-cohomology #intuition #betti-numbers
833
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Homology class and Betti number for a compact manifold with boundaries

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#general-topology #algebraic-topology #homology-cohomology #betti-numbers
3.2k
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Euler characteristic: dependence on coefficients

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#algebraic-topology #homology-cohomology #betti-numbers
406
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Two ways to split the second Betti number

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#differential-geometry #algebraic-topology #betti-numbers
723
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Betti numbers of complex "sphere"

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#algebraic-geometry #algebraic-topology #betti-numbers
158
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An example of infinite Betti number refers to G-covering, and the motivation of G-covering

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#general-topology #algebraic-topology #betti-numbers
1.3k
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On the definition of graded Betti numbers

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#abstract-algebra #commutative-algebra #graded-modules #betti-numbers
2.1k
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How does one show that definition of Betti number and its "informal definition" are equal?

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#algebraic-topology #betti-numbers
242
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Castelnuovo-Mumford regularity and Betti numbers: an existence question

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#commutative-algebra #betti-numbers
168
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Graded Betti Numbers of a Stable Monomial Ideal

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#ring-theory #commutative-algebra #ideals #monomial-ideals #betti-numbers
200
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Graded Betti Numbers of a Graded Ideal with Linear Quotients

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#ring-theory #commutative-algebra #ideals #monomial-ideals #betti-numbers
79
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Betti numbers change after homogenization

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#abstract-algebra #commutative-algebra #homological-algebra #computational-algebra #betti-numbers

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