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Weak homotopy equivalence between $\Omega \underset{\rightarrow}{\lim} \ Z_n$ and $\underset{\rightarrow}{\lim} \ \Omega Z_n$

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#algebraic-topology #homotopy-theory #cw-complexes #higher-homotopy-groups
132
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Must one space be the loop space of other

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
162
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Attaching 1-cells to CW-complex affects homotopy groups?

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#algebraic-topology #homotopy-theory #cw-complexes #higher-homotopy-groups
69
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Contractibility of CW complex without Whitehead

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#homotopy-theory #cw-complexes #higher-homotopy-groups
59
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Left homotopy groups

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#general-topology #homotopy-theory #higher-homotopy-groups
457
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How does the image of the Hurewicz map $\pi_n(X,x) \to H_n(X)$ depend upon the choice of the base point?

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
989
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Are the higher homotopy groups of a compact manifold finitely generated as $\mathbb{Z}[\pi_1]$-modules?

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#algebraic-topology #higher-homotopy-groups
45
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Weak Lefchetz for a quasiprojective variety and a non-generic hyperplane

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#algebraic-geometry #algebraic-topology #morse-theory #higher-homotopy-groups
539
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Different definitions of the minimal Chern number and the monotonicity of symplectic manifolds

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#homotopy-theory #symplectic-geometry #characteristic-classes #higher-homotopy-groups
163
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Evaluating a symplectic form on $\pi_2$ or its image through the Hurewicz map

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#homology-cohomology #homotopy-theory #symplectic-geometry #higher-homotopy-groups
163
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How do synthetic homotopy groups relate to the usual homotopy groups?

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#algebraic-topology #homotopy-theory #homotopy-type-theory #higher-homotopy-groups
157
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Behaviour of direct limits of topological spaces with respect to preimages

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#general-topology #algebraic-topology #homotopy-theory #limits-colimits #higher-homotopy-groups
122
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Higher homotopy of a wedge of $3$-sphere and Poincare homology sphere.

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#algebraic-topology #homotopy-theory #covering-spaces #higher-homotopy-groups
224
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Whitehead theorem for maps between CW-complexes

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#algebraic-topology #homotopy-theory #cw-complexes #higher-homotopy-groups
79
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Proof that higher homotopy groups of kan complexes are abelian using Eckmann-Hilton

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#algebraic-topology #homotopy-theory #simplicial-stuff #higher-homotopy-groups #homotopy-extension-property

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