Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • Galois symmetries of knot spaces

  • Part of
  • 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

  • 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 $n \leq p + 1$.

  • Finite type knot invariants and the calculus of functors

  • Ismar Volić
  • Journal:
    Compositio Mathematica / Volume 142 / Issue 1 / January 2006
    Published online by Cambridge University Press:
    13 January 2006, pp. 222-250
    Print publication:
    January 2006
    • Article
      • You have access
    • PDF
    • Export citation

  • We associate a Taylor tower supplied by the calculus of the embedding functor to the space of long knots and study its cohomology spectral sequence. The combinatorics of the spectral sequence along the line of total degree zero leads to chord diagrams with relations as in finite type knot theory. We show that the spectral sequence collapses along this line and that the Taylor tower represents a universal finite type knot invariant.