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2 results

Stability of concordance embeddings
Thomas Goodwillie, Manuel Krannich, Alexander Kupers
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View

Published online by Cambridge University Press:

20 March 2023, pp. 1-36
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We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.

Galois symmetries of knot spaces
Part of
- Differential topology
- Homotopy groups
Pedro Boavida de Brito, Geoffroy Horel
Journal:

Compositio Mathematica / Volume 157 / Issue 5 / May 2021

Published online by Cambridge University Press:

29 April 2021, pp. 997-1021

Print publication:

May 2021
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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 $(n+1)$th Goodwillie–Weiss approximation is a $p$-local universal Vassiliev invariant of degree $\leq n$ for every $n \leq p + 1$.