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Maps between cohomology groups of based loop spaces

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#algebraic-topology #homology-cohomology #loop-spaces
359
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If $H\leq G$, then $BH \to BG$ is a fiber bundle with fiber $G/H$

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#general-topology #algebraic-topology #fiber-bundles #principal-bundles #classifying-spaces
724
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Example of two spaces indisinguishable by their homology modules (with $\mathbb{Z}$ coefficients) but with different cohomology rings

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#algebraic-topology #homology-cohomology
59
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Proof verification of Simplicial homology of $M_g$

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#proof-verification #algebraic-topology #homology-cohomology #alternative-proof
1.5k
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Does there exist a continuous function from the unit interval to a circle with "closure"?

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#algebraic-topology
132
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Transitive action of $H^2(M;\Bbb Z)$ on $Spin^c$ structures over $M$

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#algebraic-topology #differential-topology #principal-bundles #spin-geometry
408
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Vanishing of Chern characters in degree below codimension of support

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#algebraic-geometry #algebraic-topology #homology-cohomology #sheaf-theory
157
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Stiefel-Whitney and Wu classes of $d$-manifold

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#algebraic-topology #differential-topology #characteristic-classes
834
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What are the Betti numbers of a double pinched torus?

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#algebraic-topology #homology-cohomology #betti-numbers
346
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Show that the rational cohomology ring $H^*(M;\mathbb{Q})$ needs at least two generators

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#group-theory #algebraic-topology #homology-cohomology
248
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How to show a simple closed curve is not nullhomotopic in the complement of another simple closed curve

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#algebraic-topology #covering-spaces
311
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Examples for short exact sequences of real vector bundles that don't split.

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#general-topology #algebraic-topology #vector-bundles
745
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Orientation and first homology

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#algebraic-topology #manifolds #differential-topology #geometric-topology
152
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regular covers for spaces with abelian fundamental group

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#general-topology #algebraic-topology
103
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Lemma 11.42 Rotman's algebraic topology

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#algebraic-topology #homotopy-theory

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