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$|\beta(s)-\alpha(x)|<d$ implies that $\beta$ is homotopic to $\alpha$.

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#general-topology #homotopy-theory
2.5k
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Why is the identity map from $S^1$ to $S^1$ not homotpic to the constant map?

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#algebraic-topology #homotopy-theory
492
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Homotopical perspective on the long exact sequence in homology and Mayer-Vietoris

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#reference-request #algebraic-topology #homotopy-theory
183
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What is the relationship between the path-loop space fibration and path induction?

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#homotopy-theory #homotopy-type-theory
696
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Group homomorphism on unit circle

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#general-topology #algebraic-topology #homotopy-theory
627
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$\mathbb{R}^{2}$ and $\mathbb{R} \times [0, +\infty]$ are homotopy equivalent, but not homeomorphic

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#general-topology #algebraic-topology #homotopy-theory
390
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When the free loop space fibration splits?

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#algebraic-topology #homotopy-theory #loop-spaces
2.5k
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cup product in cohomology ring of a suspension

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#algebraic-topology #homology-cohomology #homotopy-theory #geometric-topology #cw-complexes
60
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Simplicial function space and homotopy colimits

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#algebraic-topology #category-theory #homotopy-theory
485
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Convex Homotopy

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#general-topology #homotopy-theory
635
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Homotopy equivalence between circles

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#algebraic-topology #homotopy-theory
2.2k
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Meaning of n-connected pairs

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#general-topology #algebraic-topology #homotopy-theory
516
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complex integral of 1/z independent of choice of ellipse?

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#integration #complex-analysis #homotopy-theory
182
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Counting singularities

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#differential-geometry #differential-topology #lie-groups #homotopy-theory
1.5k
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Show that $\mathbb{R}^m$ is not homeomorphic to $\mathbb{R}^n$

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#general-topology #algebraic-topology #homotopy-theory

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