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How Bockstein homomorphism maps under Poincarè duality?

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#algebraic-topology #homology-cohomology #exact-sequence #poincare-duality
60
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Intersection number of submanifolds with boundary

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#algebraic-topology #intersection-theory #submanifold #manifolds-with-boundary #poincare-duality
139
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Composition of Gysin and restriction maps on $\ell$-adic cohomology

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#algebraic-geometry #etale-cohomology #projective-varieties #poincare-duality
50
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Correspondence between Euclidean and non-Euclidean geometries

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#geometry #noneuclidean-geometry #poincare-duality
89
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Prove/disprove that $X$ is a manifold

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#algebraic-topology #manifolds #homology-cohomology #poincare-duality
101
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If $M$ is compact connected non-orientable 3-manifold, then $H_1(M)$ is infinite.

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#algebraic-topology #manifolds #homology-cohomology #poincare-duality
71
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Faces of the cap product

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#general-topology #algebraic-topology #definition #simplex #poincare-duality
115
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Proof of Poincaré duality

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#general-topology #algebraic-topology #proof-explanation #manifolds #poincare-duality
102
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The inverse map of the Poincare duality map

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#algebraic-topology #duality-theorems #module-isomorphism #poincare-duality
57
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Let $A$ be a 2-torsion finite abelian group . Let $f: A\to (\Bbb{Q}/\Bbb{Z})^n$ be an arbitrary group homomorphism. $image(f)\le 2^n$?

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#abstract-algebra #number-theory #abelian-groups #p-adic-number-theory #poincare-duality
65
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An example of a non hausdorff space

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#general-topology #algebraic-topology #manifolds #poincare-duality #non-orientable-surfaces
80
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Intersection of submanifolds, cup products, and Poincaré duality

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#general-topology #algebraic-topology #differential-topology #transversality #poincare-duality
67
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Why is the signature of a manifold homotopy invariant?

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#algebraic-topology #differential-topology #smooth-manifolds #poincare-duality
66
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Definition of Lefschetz Number in Bott&Tu and in Gullemin&Pollack Differs by a sign?

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#algebraic-topology #differential-topology #differential-forms #intersection-theory #poincare-duality
34
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Fix points of Galois action on etale homology

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#algebraic-geometry #arithmetic-geometry #etale-cohomology #poincare-duality

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