Contents

# Contents

## Idea

Given a manifold $\Sigma$, such as the 3-sphere, its space of knots is a topological space parametrizing knots in $\Sigma$, hence something like the topological subspace

$Emb(S^1, \Sigma) \;\subset\; Maps(S^1,\Sigma)$

of the space of maps $S^1 \to \Sigma$ on those maps which are embeddings. This space is often denoted just $\mathcal{K}$.

A knot invariant is then equivalently a locally constant function on the space of knots.

## References

### Using graph complexes

Discussion of the rational homotopy type of knot spaces in terms of graph complexes:

Last revised on October 5, 2019 at 16:22:46. See the history of this page for a list of all contributions to it.