Galois symmetries of knot spaces

Abstract

We exploit the Galois symmetries of the little disks operads to show that many differentials in the Goodwillie-Weiss spectral sequences approximating the homology and homotopy of knot spaces vanish at a prime $p$. Combined with recent results on the relationship between embedding calculus and finite-type theory, we deduce that the $(n+1)$-st Goodwillie-Weiss approximation is a $p$-local universal Vassiliev invariant of degree $\le n$ for every $n\le p+1$.

arXiv comment22 pages

References in corpus (8)

• Dendroidal sets and simplicial operads
• Embeddings from the point of view of immersion theory: Part II
• Long knots and maps between operads
• Spaces of smooth embeddings and configuration categories
• The rational homology of spaces of long knots in codimension >2
• Multiple disjunction for spaces of smooth embeddings
• Embedding calculus knot invariants are of finite type
• On the formality of the little disks operad in positive characteristic

Cited by in corpus (5)

• Knotted families from graspers
• Embedding calculus and grope cobordism of knots
• Models for knot spaces and Atiyah duality
• Sinha's spectral sequence for long knots in codimension one and non-formality of the little 2-disks operad
• Graphing, homotopy groups of spheres, and spaces of long links and knots