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weak equivalence of the geometric realisation of a total singular complex and a topological space (from P.May concise course in Algebraic Topology)

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#algebraic-topology #simplicial-complex #higher-homotopy-groups #geometric-realization
528
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Does the functor $\pi_n\colon \mathsf{Top}_* \to \mathsf{Grp}$ preserve products?

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#algebraic-topology #category-theory #homotopy-theory #higher-homotopy-groups
116
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Homotopy groups in large dimensions

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#algebraic-topology #homotopy-theory #cw-complexes #higher-homotopy-groups
547
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homotopy groups of product space

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#algebraic-topology #homotopy-theory #exact-sequence #higher-homotopy-groups
139
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Modification of a CW-Complex $X$ with control over Homology groups

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#algebraic-topology #homology-cohomology #homotopy-theory #cw-complexes #higher-homotopy-groups
83
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Eckmann–Hilton Argument and magma homomorphisms

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#abstract-algebra #algebraic-topology #magma #higher-homotopy-groups
67
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Where can I get an alternative proof of this characterisation of weak equivalences?

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#algebraic-topology #homotopy-theory #cw-complexes #higher-homotopy-groups #homotopy-extension-property
97
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Calculate homotopy groups of $\mathbb{Z}_2$-equivariant loop spaces of "complex" topological spaces

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#homotopy-theory #stable-homotopy-theory #higher-homotopy-groups #equivariant-maps #equivariant-topology
71
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Kunneth and Dold-Thom

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#algebraic-topology #homology-cohomology #higher-homotopy-groups
98
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Infinite symmetric product of an $H$-space and graded product structure on homotopy groups.

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#algebraic-topology #homology-cohomology #graded-rings #higher-homotopy-groups
52
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Prove that $\pi_{2n+1}(\mathbb CP^n) \cong \mathbb Z$ using the mapping cone

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#algebraic-topology #projective-space #higher-homotopy-groups
60
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Complement of low dimension subsets and higher homotopy group

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#general-topology #algebraic-topology #differential-topology #higher-homotopy-groups
46
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Reference for Jacobi identity for general Whitehead product

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#algebraic-topology #definition #homotopy-theory #higher-homotopy-groups
56
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Map on homotopy groups induced by the swap map

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
105
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Finite CW-complex with finite homotopy groups

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#examples-counterexamples #homotopy-theory #higher-homotopy-groups

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