3 problems

Let $X$ range over real $2n$-dimensional torus manifolds corresponding to a multifan $\mathcal S_X$. Let $h_k(\mathcal S_X)=\sum_{i=k}^n(-1)^{i-k}\binom{i}{k}e_{n-i}(\mathcal S_X)$…

K-theory presentation conjecture. The ring $K^*(E(X))$ is a free $K^*(B)$-module of rank $m=\chi(X)$ and is isomorphic to $\mathfrak{S}/\mathfrak{J}$.

Minkowski-relation presentation conjecture. As a vector space, $\mathcal{F}^{2k}(X)$ is generated by the elements $\{x_I\}_{I\in K}$ subject to the Minkowski relations