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15
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Is the induced map $BX_U\to BR_U $ a homotopy equivalence?

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#algebraic-topology #homotopy-theory #simplicial-complex
258
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Postnikov tower of a CW complex is unique up to homotopy equivalence

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#algebraic-topology #homotopy-theory #cw-complexes
534
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Homotopy equivalence between connected n-dimensional CW complexes

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#algebraic-topology #homology-cohomology #homotopy-theory
619
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How to prove no homotopy of paths in $\mathbb{R}^2\setminus\{(0,0)\}$?

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#algebraic-topology #homotopy-theory
78
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What does $Ho(Top,\pi_0^{-1}(\mathcal{W}))$ look like?

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#algebraic-topology #category-theory #homotopy-theory
328
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Why do we need $A,B$ contractible for $A\cup B$ to be contractible?

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#algebraic-topology #homotopy-theory #cw-complexes
211
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Fundamental group of covering space given fundamental group of base

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#algebraic-topology #homotopy-theory #fundamental-groups
256
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Commutative diagram in defining local degree

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#algebraic-topology #homotopy-theory
705
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Attaching $2$-cell to a circle

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#algebraic-topology #homotopy-theory #cw-complexes
101
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Find the homotopy fibre of the map $\pi$

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
478
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Proof of a property of Whitehead product

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
494
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Spectral sequence for homotopy (co)limits

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#homotopy-theory #limits-colimits #spectral-sequences #spectra #cofibrations
86
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What is the homotopy that makes this diagram commutative?

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#algebraic-topology #proof-explanation #homotopy-theory
85
Views

What does $H_*(X,A) = 0$ intuitively mean?

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#homology-cohomology #homotopy-theory #group-isomorphism
136
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Existence of length-monotonic homotopy in planar domains

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#differential-geometry #homotopy-theory #euler-lagrange-equation #arc-length

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