In summary, we have introduced and studied the following objects, spaces, and maps:
Objects: is the space of all framed oriented knots in an oriented . More precisely, it is the free -module generated by framed oriented knots in an oriented .
is the free
by framed oriented knots in an oriented
precisely n double point singularities
Figure 2, modulo the co-differentiability relation
of Definition 1.2,
The Co-Derivative: The co-derivative
is the map
The Cube Ladder and Finite Type Invariants:
The n-Symbols: The space of n-symbols is the space of n-chord diagrams, as in Figure 3.
The Relator Ladder: The relator ladder is the ladder
The Primary Integrability Constraints: The primary integrability constraints are the images of the relators via the map b; that is, they are the Topological 4-Term relations of Figure 4.
The Relator Symbols and the Symbol-Level Relations: The relator symbols are diagrams of the kind appearing in Figure 7.
The Once-Reduced Symbol Space and Once Integrable Weight Systems:
The Inductive Problem:
The Lifting Problem:
Generic Symbol-Level Redundencies:
The Object-Level Redundencies:
The Redundency Problem: