The ultimate goal of this book is to explain that the Grothendieck–Teichmüller group, as
defined by Drinfeld in quantum group theory, has a topological interpretation as a group of …

The little $ N $-disks operad, $\mathcal B $, along with its variants, is an important tool in
homotopy theory. It is defined in terms of configurations of disjoint $ N $-dimensional disks …

Graduate students and researchers alike will benefit from this treatment of classical and
modern topics in homotopy theory of topological spaces with an emphasis on cubical …

We study high-dimensional analogues of spaces of long knots. These are spaces of
compactly supported embeddings (modulo immersions) of ℝ m into ℝ n. We view the space …

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 …

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 …

For any smooth manifold MM of dimension d⩾ 4 d\geqslant4, we construct explicit classes in
homotopy groups of spaces of embeddings of either an arc or a circle into MM, in every …

Goodwillie calculus is a method for analyzing functors that arise in topology. One may think
of this theory as a categorification of the classical differential calculus of Newton and …