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Homotopy group of $O(p,q)$

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#algebraic-topology #lie-groups #homotopy-theory #higher-homotopy-groups
197
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How to show that the homotopy group $\pi_4(U(3))$ of a unitary group is finite

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
110
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What can be said about the homotopy groups of $(\widetilde{K}\times X)/G$

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#algebraic-topology #homotopy-theory #fiber-bundles #fibration #higher-homotopy-groups
196
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Homotopy cardinality of fiber bundles

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#general-topology #algebraic-topology #homotopy-theory #fiber-bundles #higher-homotopy-groups
325
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Five lemma for homotopy exact sequences of triple

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#algebraic-topology #homological-algebra #homotopy-theory #higher-homotopy-groups
303
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Reflection of $S^n$ is the inverse of the identity map in $\pi_n(S^n)$

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#algebraic-topology #homotopy-theory #spheres #higher-homotopy-groups
198
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The n-sphere is not a deformation retract of the bouquet of k n-spheres

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#algebraic-topology #homotopy-theory #spheres #exterior-algebra #higher-homotopy-groups
31
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Bijection $[((X,A)),((Y \star))]\simeq[X/A,Y]^0$

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#general-topology #algebraic-topology #homotopy-theory #higher-homotopy-groups
50
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Question regarding the proof of Theorem 6.1.2 Tom Dieck

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#general-topology #algebraic-topology #homotopy-theory #higher-homotopy-groups
133
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Homotopy groups of projective Lie groups PO(N), PSO(N), and PSpin(N)

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#lie-groups #homotopy-theory #quotient-spaces #fundamental-groups #higher-homotopy-groups
268
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Can the fundamental group $\pi_1(X)$ of topological space $X$ be non-abelian? or be continuous?

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#general-topology #algebraic-topology #homotopy-theory #topological-groups #higher-homotopy-groups
274
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Understanding $CW$ approximation theorem.

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#algebraic-topology #modules #homotopy-theory #cw-complexes #higher-homotopy-groups
70
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Understanding Theorem 6.3.1 Tom Dieck

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#general-topology #algebraic-topology #proof-explanation #higher-homotopy-groups
35
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Is an homotopy class represented by the homotopy class of inclusion as subspace?

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#general-topology #algebraic-topology #homotopy-theory #fundamental-groups #higher-homotopy-groups
82
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Covering ${\Bbb R}^{3}$ by disoint circles.

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#general-topology #euclidean-geometry #homotopy-theory #higher-homotopy-groups

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