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Results tagged with loop-spaces
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user 2039
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.
8
votes
Is there a good way to understand the free loop space of a sphere?
The next best thing to the knowledge of a CW-structure is probably the knowledge of the integral homology (not just the Betti numbers). Perhaps Ziller was the first to compute it in The Free Loop Spac …
- 12.1k
6
votes
Example s.t. the unbased loop-space is not $\Omega X \times X$
The unbased loop space is also known as the free loop space and is often also denoted by $LX$ or $\Lambda X$. If you compute the homology of $LX$ (which might be difficult in general) you will often s …
- 12.1k