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Submanifold generators that correspond to Stiefel Whitney class of $\mathbb{RP}^n$

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#differential-geometry #algebraic-topology #homology-cohomology #geometric-topology #characteristic-classes
240
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Submanifold generator and its Poincaré dual in a 5-dimensional real projective space

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#algebraic-topology #manifolds #homology-cohomology #geometric-topology #projective-space
430
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How are the homology groups of map space related to the "factors"?

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#reference-request #algebraic-topology #homology-cohomology #homotopy-theory
78
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Action of quadratic Casimir on cochain/cohomology spaces

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#modules #representation-theory #lie-algebras #homology-cohomology #lie-superalgebras
113
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What is the induced isomorphism of a handle decomposition $X_k=X_{k-1}\cup H^{\lambda_k}$, $X_0=D^m$ given by the long exact Mayer-Vietoris sequence?

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#algebraic-topology #homology-cohomology
76
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Poincaré dual of $H^1(M,\mathbb{Z}_2)$ for a $\frac{\mathbb{CP}^2\times S^1}{\tau}$

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#algebraic-topology #manifolds #homology-cohomology #geometric-topology #quotient-spaces
362
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de Rham cohomology of vector bundles: advantages of different definitions of compact vertical cohomology

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#algebraic-topology #differential-topology #homology-cohomology #vector-bundles
184
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How to show a morphism $f^•: A^•\to B^•$ of complexes induce the morphism of cohomology objects $H^i(A^•)\to H^i(B^•)$?

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#algebraic-geometry #category-theory #homology-cohomology #abelian-categories
218
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Motivation for cochains, cocycles and coboundaries

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#abstract-algebra #reference-request #homology-cohomology #intuition #group-cohomology
85
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Poincaré dual of the trivial class $H^1(\mathbb{RP}^5,\mathbb{Z}_2)$

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#algebraic-topology #manifolds #homology-cohomology #geometric-topology #projective-space
69
Views

Proof in Lee's Introduction to Topological manifolds

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#homology-cohomology #homological-algebra #homotopy-theory
40
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Poincaré dual of the generators of $H^d(S^5/\mathbb{Z}_4,\mathbb{Z}_4)$

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#algebraic-topology #manifolds #homology-cohomology #geometric-topology #quotient-spaces
70
Views

looking for flabby sheaf resolutions

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#abstract-algebra #category-theory #homology-cohomology #sheaf-theory #d-modules
475
Views

The three definitions of Cech cohomology (simplical complex vs. presheaf vs. sheaf)

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#algebraic-topology #homology-cohomology #sheaf-cohomology #de-rham-cohomology
552
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Metaplectic group is the unique double covering of symplectic group

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#algebraic-topology #homology-cohomology #symplectic-geometry

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