Vogel’s conjecture on the algebra structure of top-degree odd graph cohomology

Prove that the top-degree 2g−2 odd commutative graph cohomology H^{2g−2}(GC_−) forms the specific commutative algebra proposed by Vogel (2011), thereby establishing the conjectured algebraic identification of this cohomology in degree 2g−2.

Background

The odd commutative graph complex GC_− plays a central role in knot theory and finite type invariants. Many cohomology classes are known in its top degree 2g−2 via connections to Chern–Simons theory.

Vogel conjectured that, in this top degree, the odd commutative graph cohomology has the structure of a specific commutative algebra. Confirming this would precisely characterize the algebraic structure of H^{2g−2}(GC_−).