In many areas of mathematics some “higher operations” are arising. These havebecome so
important that several research projects refer to such expressions. Higher operationsform …

With hundreds of worked examples, exercises and illustrations, this detailed exposition of
the theory of Vassiliev knot invariants opens the field to students with little or no knowledge …

We model the homotopy fiber $ E_m $ of the inclusion of the space of long knots in
dimension $ m $ into the corresponding space of immersions, through an operad structure …

We continue our investigation of spaces of long embeddings (long embeddings are high-
dimensional analogues of long knots). In previous work we showed that when the …

We present two models for the space of knots which have endpoints at fixed boundary points
in a manifold with boundary, one model defined as an inverse limit of spaces of maps …

We determine the rational homology of the space of long knots in ℝ d for d≥ 4. Our main
result is that the Vassiliev spectral sequence computing this rational homology collapses at …

Haefliger proved that the isotopy classes of smooth embeddings of S j in S n form a group
provided nj> 2, with the connect-sum as multiplication. This paper starts with a new proof of …

This paper gives a partial description of the homotopy type of K, the space of long knots in
R3. The primary result is the construction of a homotopy equivalence K≃ C2 (P⊔{∗}) where …

The paper describes a natural splitting in the rational homology and homotopy of the spaces
of long knots. This decomposition presumably arises from the cabling maps in the same way …

This paper gives a detailed description of the homotopy type of 𝒦, the space of long knots in
ℝ3, the same space of knots studied by Vassiliev via singularity theory. Each component of …