Stable independence conjecture for the strata and boundary algebras

Let

\lambda_{2i+1}$ denote the odd Chern-character generators in stable cohomology, let the classes of boundary strata generate the strata algebra, and let $D_m$ denote the boundary divisor classes. **Stable independence conjecture.** There are no stable relations in either the strata algebra or the boundary algebra: no polynomial in the

\lambda_{2i+1}$and the classes of boundary strata, and no polynomial in the$D_m$, is identically zero for$g$ sufficiently large. This predicts algebraic independence of the indicated stable generators and rules out further stable relations among the boundary and strata classes.