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100
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Hatcher 4.2.19 homotopy group of skeleton of $K(G,1)$

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#algebraic-topology #cw-complexes #higher-homotopy-groups #eilenberg-maclane-spaces
107
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Ranking topological invariants by "strength?"

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#algebraic-topology #homology-cohomology #homotopy-theory #stable-homotopy-theory #higher-homotopy-groups
101
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Computing the homotopy groups $\pi_n(\mathbb RP^2 \times \mathbb S^3).$

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#algebraic-topology #homology-cohomology #homotopy-theory #group-cohomology #higher-homotopy-groups
99
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Is the Whitehead product $[\iota_2, \eta] : \pi_4\mathbb{S}^2$ trivial?

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#algebraic-topology #higher-homotopy-groups
119
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A possible error in May's Concise Algebraic Topology (prespectra)

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#algebraic-topology #homotopy-theory #stable-homotopy-theory #higher-homotopy-groups
123
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What is the value of homotopy group $\pi_1(SU(2)\times U(1))$

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#algebraic-topology #lie-groups #mathematical-physics #fundamental-groups #higher-homotopy-groups
85
Views

"Homotopy" group with the torus $\mathbb{T}^2$ as a domain and the sphere $\mathbb{S}^2$ as codomain

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#algebraic-topology #homotopy-theory #mathematical-physics #higher-homotopy-groups
49
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For an explicit mapping $S^m\to S^6$ for $m<12$, how can we understand whether it is homotopy zero?

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#homotopy-theory #geometric-topology #higher-homotopy-groups
53
Views

Proving that $\pi_q(T(S^m)\setminus f^{-1}(A))\cong \pi_q(S^m\setminus A)$ for $q\ge 1$

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#differential-geometry #algebraic-topology #higher-homotopy-groups
132
Views

Higher Homotopy Groups of Spheres: Motivation and State of the Art

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
52
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S : ∞-Grpd₀ ⭢ ∞-Grpd₀ such that Homology of X is the homotopy of SX?

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#homology-cohomology #abelian-groups #cw-complexes #higher-homotopy-groups
64
Views

What is the difference between an E∞-Space and an H-Space

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#homotopy-theory #higher-homotopy-groups
47
Views

Homotopy sequence of a weak fibration with a section

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#algebraic-topology #homotopy-theory #exact-sequence #higher-homotopy-groups
48
Views

Is openness crucial in Puppe's proof of the Blakers-Massey Theorem?

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
12
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Show that the pushout of this specific simplicial map induces an isomorphism on the $n$th simplicial homotopy group.

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#limits-colimits #simplicial-stuff #higher-homotopy-groups

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