Raoul Bott: Collected Papers pp 317-335 | Cite as

# [108] Configuration Spaces and Imbedding Invariants

**Introduction**

For the past two years I have been trying to understand the new physics-inspired invariants of t hree-manifolds and knots in terms of concepts more congenial to the classical topologist.

In [K] Kontsevich indicates a method for defining a set of invariants for 3-manifolds *M*, which presumably recreates the asymptotic invariants of the Chern-Simons theory at the trivial representation of π_{1}*(M)*, entirely in terms of the De Rham Theory of Configuration spaces of *M*. It therefore seemed plausible, ℝ^{3} being simply con nected, that a similar approach would work for knots in ℝ^{3}, and in our recent paper [B-T] Cliff Taubes and I showed that this is indeed the case. Since t hen we have noted that this method yields potential invariants also for higher-dimensional knots of *S*^{2k - l} in ℝ^{2k+l}, and the first of these will be presented in section 3. How ever, in this account I will mainly concentrate on the classical case and try and fit our constructions into the picture as it emerges...

## **References**

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