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15
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Show that two for two functions $f, g$ there exists a point which has the same image in $\mathbb{S}^{2n}$.

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#general-topology #algebraic-topology #homology-cohomology #homotopy-theory
90
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$S^1$ has no deformation retracts other than itself

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#general-topology #algebraic-topology #homotopy-theory #fundamental-groups #retraction
59
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Classifying cofibrations in Mor(M) where M is a model category

Published on
#category-theory #homotopy-theory #model-categories
59
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Replacing extension with left-right projective extensions

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#homological-algebra #homotopy-theory #hochschild-cohomology
58
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Hatcher algebraic topology 4.3.10

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#algebraic-topology #homotopy-theory #group-actions #fiber-bundles
220
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Complex of sheaves, Eilenberg-MacLane spectra and hypercohomology

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#algebraic-topology #category-theory #homotopy-theory #sheaf-cohomology #spectra
62
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Image of paths closed in a covering

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#homotopy-theory #covering-spaces #path-connected
43
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Homotopy equivalence vs deformation retract for analytic spaces

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#algebraic-topology #homotopy-theory #real-algebraic-geometry #retraction
129
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Prove that $\mathbb{R}$ is contractible

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#general-topology #algebraic-topology #homotopy-theory
48
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Prove that there is no function $f: B[0,1] \to \mathbb{S}^1$ such that $\left.f\right |_{\partial B[0, 1]} = id$

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#general-topology #algebraic-topology #homotopy-theory #fundamental-groups
60
Views

Equivalence between two definitions of $J$-homomorphisms.

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#algebraic-topology #homotopy-theory
86
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"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
170
Views

Generalized wedge sums of multiple $S^n$

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#geometry #algebraic-topology #homotopy-theory #fundamental-groups
60
Views

No homotopy with the identity of the unit circle

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#general-topology #algebraic-topology #homotopy-theory #retraction
63
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2nd Homotopy group of homogeneous space constructed from SO(n)

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#lie-groups #homotopy-theory #homogeneous-spaces

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