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15
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Is composing homotopies of spheres bilinear?

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#algebraic-topology #homotopy-theory #higher-homotopy-groups
156
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Why model categories in theory of stacks?

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#algebraic-topology #homotopy-theory #higher-category-theory #model-categories #topological-stacks
49
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$f:X\to Y$ extends to a map $Z\to Y$ iff $f_*[g] = 0$

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#algebraic-topology #homotopy-theory #quotient-spaces #universal-property #higher-homotopy-groups
209
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Show that every contractible space is connected.

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#general-topology #algebraic-topology #homotopy-theory
330
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Cofibrant objects are isomorphic to their cofibrant replacements

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#category-theory #homotopy-theory #model-categories
65
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Postnikov sections are monoidal functor or not?

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#algebraic-topology #homotopy-theory #stable-homotopy-theory
42
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Question regarding surjectivity of induced homormophism in an old version of Hatcher's proof of Prop. 4.13

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#algebraic-topology #homotopy-theory #group-homomorphism #higher-homotopy-groups
65
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Homotopic functions-proof

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#algebraic-topology #homotopy-theory
37
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CW approximation: why does $S^{n+1}\to X$ qualify as an attaching map for attaching $S^{n+1}$ to another space $Z$?

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#homotopy-theory #cw-complexes #higher-homotopy-groups
55
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Understanding the fulfillment of a condition required for applying the pasting lemma.

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#general-topology #continuity #proof-explanation #homotopy-theory
48
Views

Higher homotopy groups of a string complement in a cylinder.

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#algebraic-topology #homotopy-theory #knot-theory
79
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Does a deformation retraction of $X$ onto a subspace $A\subset X$ induce an isomorphism $\pi_n(X) \to \pi_n(A)$?

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#homotopy-theory #group-isomorphism #retraction #higher-homotopy-groups
58
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Is "Darboux" homotopy trivial?

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#homotopy-theory #connectedness
60
Views

Equivalence of homotopy, relative homotopy and continuous extension

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#general-topology #algebraic-topology #homotopy-theory
301
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prove that the reduced join of 2 spaces is homeomorphic to the reduced suspension of the smash of them.

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#general-topology #algebraic-topology #proof-explanation #homotopy-theory

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