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Cohomology of colimit is limit of cohomology ? (group cohomology)

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#homology-cohomology #homotopy-theory #group-cohomology #limits-colimits
102
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$H_n(X, F_p) = 0$ implies $H_n (X,Q)=0$ for certain CW-complexes $X$

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#algebraic-topology #homology-cohomology #cw-complexes
181
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Can someone please explain the map $S:C_n(X) \to C_n(X)$ from Hatcher's AT page 122?

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#abstract-algebra #algebraic-topology #proof-explanation #homology-cohomology #homological-algebra
249
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First and third homology of $S^5/Z_q$ and Leray spectral sequence

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#proof-verification #algebraic-geometry #algebraic-topology #homology-cohomology #spectral-sequences
33
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How is $\tilde H_i(S^n) =0$ for $i \ne n$?

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#proof-verification #algebraic-topology #homology-cohomology
214
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Why is $H_0(X,x_0) \ne H_0(X)$

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#algebraic-topology #homology-cohomology #intuition
118
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Compute Cech cohomology of a subscheme defined by a homogeneous equations in $P^2_k$

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#algebraic-geometry #homology-cohomology
166
Views

What is the tensor product over in Künneth’s formula

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#homology-cohomology
266
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Cohomology of spectra as free modules over Steenrod Algebra

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#algebraic-topology #homology-cohomology #spectral-sequences #eilenberg-maclane-spaces #spectra
116
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Homology of the Torus over a Module

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#general-topology #group-theory #algebraic-topology #homology-cohomology #free-modules
156
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Is every 3-dimensional Poincaré complex a 3-dimensional topological variety?

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#algebraic-topology #differential-topology #homology-cohomology #low-dimensional-topology #poincare-duality
119
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homology of a subspaces of product of circles.

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#algebraic-topology #manifolds #homology-cohomology
86
Views

Lemma for Hurewicz Theorem (Bredon)

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#algebraic-topology #homology-cohomology #simplex #simplicial-stuff
62
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Confusion regarding sheaf cohomology and singular cohomolgy

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#algebraic-geometry #homology-cohomology #algebraic-curves #sheaf-cohomology
52
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Modifying long exact sequences

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#abstract-algebra #homology-cohomology #homological-algebra #abelian-groups #exact-sequence

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