Homology-dimension conjecture for images of stable perturbations on ICIS

Let $f\colon (X,S)\to(\mathbb{C}^{p},0)$ be a map germ of finite $\mathscr{A}_e$-codimension, where $X$ is an ICIS of dimension $n<p$. Let $d(f)$ and $s(f)$ denote the quantities used in the source. Homology-dimension conjecture. The reduced integer homology of the image of a stable perturbation of $(X,f)$ is zero except possibly in dimensions

$$p-k(p-n)k+k-1$$

for all $2\leq k\leq d(f)$, in dimension $d(f)-1$ if $s(f)>d(f)$, and in dimension $n$ if $X$ is non-smooth. The source presents this as an expected statement following a remark that the preceding theorem may not be sharp; no resolution status is supplied.