List questions from loop-spaces

Published on 25 Sep 2011 - 17:32

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Showing that the loopspace $\Omega S^{\infty}$ is homotopic to $S^{\infty}$.

Published on 13 Apr 2012 - 20:37

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Why is the recognition principle important?

Published on 25 Mar 2026 - 15:57

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What kind of information is given by the n-th homotopy group for n>=2?

Published on 26 Nov 2012 - 5:18

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Γ-spaces and operads

Published on 25 Mar 2026 - 15:57

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It is possible that $ X \simeq \Omega X $ and that $ X \simeq \Omega^ 2X $?

Published on 01 Sep 2020 - 10:01

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How does multiplication in $\Omega X$ induce multiplication for chains of $\Omega X$?

Published on 15 Sep 2020 - 21:45

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Why are loop spaces $\Omega Y$ examples of grouplike spaces?

Published on 17 Sep 2020 - 10:15

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Mahowald-Hopkins theorem

Published on 25 Mar 2026 - 15:59

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How to reconstruct a closed loop like a circle or a loop with continuous curvature change i.e. arbitrary shape by using the Frenet-Serret equation

Published on 24 Oct 2020 - 20:02

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Classifying spaces of $E_1$-spaces

Published on 24 Oct 2020 - 22:36

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Is the action functional "locally well defined up to an additive constant"?

Published on 30 Oct 2020 - 19:17

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How can I show that $X_l$ and $X_{f \circ l}$are homotopy equivalent?

Published on 10 Jan 2021 - 4:00

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Reference for first appearance of Samelson product

Published on 25 Mar 2026 - 12:24

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Fourier expansion of (small perturbations of constant) loops

Published on 16 Feb 2021 - 12:08

List Question

Non-vanishing of homology of loop spaces

Showing that the loopspace $\Omega S^{\infty}$ is homotopic to $S^{\infty}$.

Why is the recognition principle important?

What kind of information is given by the n-th homotopy group for n>=2?

Γ-spaces and operads

It is possible that $ X \simeq \Omega X $ and that $ X \simeq \Omega^ 2X $?

How does multiplication in $\Omega X$ induce multiplication for chains of $\Omega X$?

Why are loop spaces $\Omega Y$ examples of grouplike spaces?

Mahowald-Hopkins theorem

How to reconstruct a closed loop like a circle or a loop with continuous curvature change i.e. arbitrary shape by using the Frenet-Serret equation

Classifying spaces of $E_1$-spaces

Is the action functional "locally well defined up to an additive constant"?

How can I show that $X_l$ and $X_{f \circ l}$are homotopy equivalent?

Reference for first appearance of Samelson product

Fourier expansion of (small perturbations of constant) loops

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