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How does hocolim relate to Hom?

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#algebraic-topology #category-theory #homotopy-theory #simplicial-stuff
2.2k
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Why is Top a model category?

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#algebraic-topology #category-theory #homotopy-theory #model-categories
1k
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How to prove a manifold is simply connected?... using geometry

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#differential-geometry #algebraic-topology #homotopy-theory #curvature
499
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Chromatic Filtration of Burnside Ring

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#group-theory #algebraic-topology #category-theory #homotopy-theory #algebraic-k-theory
183
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Local injective model structure for simplicial presheaves

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#homotopy-theory #simplicial-stuff
860
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What's stopping me from choosing the nth Eilenberg Mac Lane space to be the following simplicial abelian group?

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#algebraic-topology #homotopy-theory #simplicial-stuff #eilenberg-maclane-spaces
1.5k
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Homotopy equivalence of two different gluings of $B^n$ and an arbitrary space $X$

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#algebraic-topology #homotopy-theory
172
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Filtration in the Serre SS

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#algebraic-topology #homological-algebra #homotopy-theory
1.1k
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Nine lemma in Triangulated categories

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#algebraic-topology #homotopy-theory #triangulated-categories
855
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What are the ramifications of the fact that the first homotopy group can be non-commutative, whilst the higher homotopy groups can't be?

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#algebraic-topology #homotopy-theory #groupoids
7.4k
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Proof that retract of contractible space is contractible

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#general-topology #algebraic-topology #homotopy-theory
633
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Degree of a map between product of manifolds

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#differential-topology #manifolds #homotopy-theory
439
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How can we detect the existence of almost-complex structures?

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#algebraic-topology #homotopy-theory #characteristic-classes #almost-complex
171
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Homotopy class representative

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#homotopy-theory
701
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every map can be replaced by a weakly equivalent fibration

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#algebraic-topology #homotopy-theory

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