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15
126
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Why is a sphere necessarily a n-cell glued to a 0-cell?

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#homotopy-theory #spherical-geometry #spheres #cw-complexes
247
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How to define and handle lower homotopy groups?

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#algebraic-topology #homotopy-theory #geometric-topology
169
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Continuity of Homotopy of paths

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#general-topology #algebraic-topology #homotopy-theory
910
Views

Fundamental group of torus with 2-cell attached

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#group-theory #algebraic-topology #homotopy-theory #normal-subgroups #fundamental-groups
505
Views

Fixed-Endpoint Homotopy for Loops to their Starting/Ending Points

Published on
#limits #multivariable-calculus #continuity #homotopy-theory
100
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In showing $\pi_2(X, x_0) \cong \pi_2(X, x_1)$, why don't we need a reverse path?

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#general-topology #algebraic-topology #proof-explanation #intuition #homotopy-theory
111
Views

If $A \subset X$ is contractible, then is $X \setminus A$ homotopy equivalent to $X \setminus a_0$?

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#general-topology #algebraic-topology #homotopy-theory
125
Views

Are there any non-trivial group extensions of $SU(N)$?

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#algebraic-topology #homotopy-theory #exact-sequence #characteristic-classes #group-extensions
92
Views

Finite cover, homotopy group $\pi_1$ and group extension

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#general-topology #algebraic-topology #lie-groups #homotopy-theory #exact-sequence
407
Views

Fundamental group of the $\text{Fivebrane}(n)$, $\text{String}(n)$, $\text{Spin}(n)$, ${SO}(n)$, ${O}(n)$

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#algebraic-topology #homotopy-theory #fundamental-groups
221
Views

Is this the correct homotopy rel $\{0,1\}$?

Published on
#proof-verification #algebraic-topology #homotopy-theory
407
Views

Using gluing/pasting lemma to show two paths are homotopic?

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#elementary-set-theory #proof-verification #algebraic-topology #homotopy-theory
38
Views

What is the $*$ in topological maps? For example $T(x,*) = (*,x)$ and $T(*,y) = (y,*)$?

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#general-topology #homology-cohomology #homotopy-theory
122
Views

Fibrations in left Bousfield localization

Published on
#homotopy-theory #model-categories
199
Views

Help with understanding homotopy commutative diagrams.

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#general-topology #homology-cohomology #homotopy-theory

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