Long knots and maps between operads

By W. Dwyer, Kathryn Hess. 2010

76 citations recorded by the source corpus.

We identify the space of tangentially straightened long knots in R^m, for m greater than or equal to 4, as the double loops on the space of derived operad maps from the associative operad into a version of the little m-disk operad. This verifies a conjecture of Kontsevich, Lambrechts, and Turchin.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5e087847a6f3b0f52c6e006bf919e7770ad5329e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Michael Weiss
2. Pedro Boavida de Brito
3. Thomas Willwacher
4. Victor Turchin
5. Benoit Fresse
6. John E. Harper

In Mathematical Physics

1. Thomas Willwacher
2. Benoit Fresse
3. Pedro Boavida de Brito
4. Michael Weiss
5. Victor Turchin
6. Søren Galatius
7. O. Randal-Williams
8. G. Arone

In Statistical and Nonlinear Physics

1. Michael Weiss
2. Pedro Boavida de Brito
3. Thomas Willwacher
4. Benoit Fresse

Citations in the corpus

• Spaces of smooth embeddings and configuration categories (2015, methodology): “It improves on some corollaries of related theorems in the work of Dwyer-Hess [13, 14], Arone-Turchin [3] and Turchin [35].”
• The rational homotopy of mapping spaces of E${}_n$ operads (2017, background): “This comparison statement was first established in the case m = 1, at the level of the limit (9) in [18], and at the level of the towers in [49].”