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15
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Is $Cat_{\Delta}$ enriched over itself?

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#homotopy-theory #simplicial-stuff #higher-category-theory
236
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Wedge of aspherical spaces

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#algebraic-topology #homotopy-theory
213
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Prove that $S^n /\{p,q\}$ is homotopy equivalent to $S^n \vee S^1$.

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#algebraic-topology #homotopy-theory
136
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Prove that $λ(A)^+ : S^n → S^n$ (the map induced on one-point compactifications) is homotopic to identity if $\det(A) > 0$

Published on
#linear-algebra #algebraic-topology #homotopy-theory
942
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How to prove (rigorously) that these spaces are homotopy equivalent?

Published on
#general-topology #algebraic-topology #homotopy-theory
266
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Example of a fibration that is not a fibre bundle

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#algebraic-topology #homotopy-theory
81
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Retract of Compact $2$-manifold

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#general-topology #algebraic-topology #homotopy-theory #compact-manifolds
44
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Let $A ∈ SO(n+1)$ and write $τ(A)$ for the induced map $S^n → S^n$. Prove that $τ(A)\simeq id$

Published on
#differential-geometry #algebraic-topology #homotopy-theory
922
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How to show that S^1 is not contractible just by definition without going into Fundamental group.

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#algebraic-topology #homotopy-theory
142
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understanding Thom's theorem for $\mathrm{MU}$ and Milnor-Novikov's result.

Published on
#algebraic-topology #homology-cohomology #homotopy-theory
1.6k
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Homotopy class of map from torus to sphere?

Published on
#algebraic-topology #differential-topology #homotopy-theory
156
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Classifying map for the hyperplane bundle

Published on
#algebraic-topology #homotopy-theory #vector-bundles #classifying-spaces
186
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When is commuting in $\pi_1$ equivalent to commuting up to homotopy?

Published on
#algebraic-topology #homotopy-theory
45
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Is connectedness needed in this statement?

Published on
#algebraic-topology #homotopy-theory
192
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Calculate homotopy of $S^2$ relative to great circle using exact sequence

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#algebraic-topology #homotopy-theory #exact-sequence

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