Knotted families from graspers

Abstract

For any smooth manifold $M$ of dimension $d\ge 4$ we construct explicit classes in homotopy groups of spaces of embeddings of either an arc or a circle into $M$, in every degree that is a multiple of $d-3$, and show that they are detected in the Taylor tower of Goodwillie and Weiss. The classes are obtained from families of string links constructed in the $d$-ball.

arXiv comment32 pages, 17 figures. v2: Shortened title, improved exposition, new figures, added a corollary about string links. Version accepted for publication in J. Topol

References in corpus (11)

• Claspers and finite type invariants of links
• Embeddings from the point of view of immersion theory: Part I
• Embeddings from the point of view of immersion theory: Part II
• Configuration spaces and Vassiliev classes in any dimension
• A family of embedding spaces
• Multiple disjunction for spaces of smooth embeddings
• Nontrivial classes in $H^{\ast }(Imb(S^1,{\mathbb{R}}^n))$ from nontrivalent graph cocycles
• Non-trivalent graph cocycle and cohomology of the long knot space
• Galois symmetries of knot spaces
• On homotopy groups of spaces of embeddings of an arc or a circle: the Dax invariant
• Lin-Wang type formula for the Haefliger invariant

Cited by in corpus (3)

• Diffeomorphisms of 4-manifolds from graspers
• Embedding calculus and grope cobordism of knots
• Graphing, homotopy groups of spheres, and spaces of long links and knots