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Results tagged with loop-spaces
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user 3634
The loop space $Ω_X$ of a pointed topological space $X$ is the space of based maps from the circle $\mathbb S^1$ to $X$ with the compact-open topology.
2
votes
Loopspace of an Eilenberg Maclane space K(G,n)
If $X$ is $(n-1)$-connected, and $Y$ is a space with $\pi_n(Y) \cong G$ and no other nontrivial homotopy groups, then the map $[X, Y] \to \mathrm{Hom}(\pi_n(X), G)$ is a bijection (by elementary obst …
- 12.5k
1
vote
Accepted
Commutativity of a diagram of boundary morphisms from the long exact sequence of homotopy gr...
The boundary map of homotopy groups is induced by a map $\partial : \Omega Y \to F$
of spaces; then the commutativity follows from the naturality of the
isomorphism $\pi_n \circ \Omega \cong \pi_{n+ …
- 12.5k