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Showing that $\pi_n(X,v)$ satisfies inverse axiom.

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#homotopy-theory #simplicial-stuff #simplicial-complex #higher-category-theory #higher-homotopy-groups
137
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Explicit isomorphism $\pi_{n+1}(\mathbb{RP}^n) \cong \pi_1(\mathbb{RP}^{n-1})$

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#general-topology #algebraic-topology #homotopy-theory #projective-space #higher-homotopy-groups
818
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How does the Hopf map generate $\pi_3(S^2)$?

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#general-topology #algebraic-topology #hopf-fibration #higher-homotopy-groups
37
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How to show that : $ \mathrm{Hot} \simeq W_{ \infty }^{-1} \mathcal{T} \mathrm{op} $?

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#homotopy-theory #cw-complexes #higher-category-theory #higher-homotopy-groups
212
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Space of Non-Surjective maps between Spheres

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#algebraic-topology #homotopy-theory #geometric-topology #higher-homotopy-groups
353
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Is a formula for the *number* of Lyndon words of a fixed length over a given number of generators known?

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#combinatorics #homotopy-theory #spheres #higher-homotopy-groups #lyndon-words
508
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Allen Hatcher chapter 4 exercise 17

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#algebraic-topology #higher-homotopy-groups
172
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Compute $\pi_{2}(S^2 \vee S^2).$

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
445
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$\pi_1(A,x_0)$ acts on the long exact sequence of homotopy groups for $(X,A,x_0)$

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
176
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Bijection between homotopy classes

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
112
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$\pi_n((S^1 \vee S^n)\cup e^{n+1})$, Example 4.35, Hatcher, Algebraic Topology

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
140
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Boundary map between homotopy groups

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#algebraic-topology #exact-sequence #higher-homotopy-groups
375
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Allen Hatcher algebraic topology proof of theorem 4.5 Whitehead

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#general-topology #algebraic-topology #higher-homotopy-groups
100
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Find the homotopy fibre of the map $\pi$

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
474
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Proof of a property of Whitehead product

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#algebraic-topology #homotopy-theory #higher-homotopy-groups

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