Quantization of the Algebra of Chord Diagrams

Abstract

In this paper we define an algebra structure on the vector space $L$ generated by links in the manifold $\Sigma \times [0,1]$ where $\Sigma $ is an oriented surface. This algebra has a filtration and the associated graded algebra $L_{Gr}$ is naturally a Poisson algebra. There is a Poisson algebra homomorphism from the algebra of chord diagrams $ch$ on $\Sigma $ to $L_{Gr}$. We show that multiplication in $L$ provides a geometric way to define a deformation quantization of the algebra of chord diagrams, provided there is a universal Vassiliev invariant for links in $\Sigma\times [0,1]$. The quantization descends to a quantization of the moduli space of flat connections on $\Sigma $ and it is universal with respect to group homomorphisms. If $\Sigma $ is compact with free fundamental group we construct a universal Vassiliev invariant.

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 103,005

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

Analytics

Added to PP
2017-06-17

Downloads
5 (#1,772,178)

6 months
1 (#1,588,578)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references