## Open problems ## See [[open problems]] ## Useful constructions ## * [[Homotopy pushout]] $Y \sqcup^X Z$ * [[Join]] $ X * Y$ * [[Suspension]] $\Sigma X$ * [[Homotopy fiber]] * [[Smash product]] $X \wedge Y$ * [[Eilenberg Maclane spaces]] $K(G,n)$ * [[James construction]] $J(X) \simeq \Omega \Sigma X$ * [[Hopf construction]] H-space on $A$ gives fibration $A \to A * A \to \Sigma A$ * [[Localization]] * [[Whitehead product]] * [[Homology]] * [[Cohomology]] $H^n(X;A) \equiv \| X \to K(G,n) \|_0$ * [[loop space of a wedge of circles]] ## Useful references ## * [On the homotopy groups of spheres in homotopy type theory](https://arxiv.org/abs/1606.05916)