Some Dimensions of Spaces of Finite Type Invariants of Virtual Knots

Abstract

We compute many dimensions of spaces of finite type invariants of virtual knots (of several kinds) and the dimensions of the corresponding spaces of “weight systems,” finding everything to be in agreement with the conjecture that “every weight system integrates.”

2000 AMS Subject Classification:

• 57M25

Keywords:

• virtual knots
• Reidemeister moves
• finite type invariants
• weight systems
• Polyak algebra

Acknowledgments

We thank Bradford Hovinen, B. David Saunders, and William Turner, of Project LinBox, for helping us with sparse matrix computations; Karene Chu and A. Referees for some comments; and Carlo Petronio, at the University of Pisa, for allowing Fionntan Roukema the freedom to partake in the project. This work was partially supported by NSERC grant RGPIN 262178.

Notes

¹This paper, programs, and related documentation are available online at http://www.math.toronto.edu/drorbn/papers/v-Dims/ .

²An alternative notion of finite type invariants of virtual knots is given in [Kauffman 99].

³Available online at http://www.linalg.org.