Some Dimensions of Spaces of Finite Type Invariants of Virtual Knots
Dror Bar-Natan, Iva Halacheva, Louis Leung, and Fionntan Roukema
TL;DR
This paper computes the dimensions of spaces of finite type invariants and weight systems for virtual knots, supporting the conjecture that all weight systems can be integrated into invariants.
Contribution
It provides extensive calculations of these dimensions for various types of virtual knots, confirming the conjecture that every weight system integrates.
Findings
Dimensions of spaces of invariants match those of weight systems.
Results support the conjecture that every weight system integrates.
Computations cover several kinds 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".
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Taxonomy
TopicsGeometric and Algebraic Topology · Computational Geometry and Mesh Generation · Homotopy and Cohomology in Algebraic Topology