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 show that the zeroth cohomology of M. Kontsevich's graph complex is isomorphic to the
Grothendieck–Teichmüller Lie algebra grt _1 grt 1. The map is explicitly described. This …

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 express the rational homotopy type of the mapping spaces $\mathrm {Map}^ h (\mathsf
D_m,\mathsf D_n^{\mathbb Q}) $ of the little discs operads in terms of graph complexes …

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 study the cohomology of complexes of ordinary (non-decorated) graphs, introduced by
M. Kontsevich. We construct spectral sequences converging to zero whose first page …

We provide a generating function for the (graded) dimensions of M. Kontsevich's graph
complexes of ordinary graphs. This generating function can be used to compute the Euler …

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 …

We show that the Hochschild-Pirashvili homology on any suspension admits the so called
Hodge splitting. For a map between suspensions $ f\colon\Sigma Y\to\Sigma Z $, the …

Context-free manifold calculus and the Fulton--MacPherson operad Page 1 msp Algebraic
& Geometric Topology 13 (2013) 1243–1271 Context-free manifold calculus and the Fulton–MacPherson …