The adjunction inequality for the Rasmussen invariant in negative-definite four-manifolds

Let $W=(\#^r\overline{\mathbb{CP}^2})\setminus B^4$ for some $r\geq 0$. Let $L\subset\partial W=S^3$ be a link, and let $\Sigma\subset W$ be a properly, smoothly embedded oriented surface with no closed components such that $\partial\Sigma=L$. The notation $[\Sigma]$, $|[\Sigma]|$, and $[\Sigma]\cdot[\Sigma]$ denotes the homology class of $\Sigma$, its norm as used in the paper, and its self-intersection, respectively.

Adjunction conjecture for $s$.

$$s(L)\leq 1-\chi(\Sigma)-\left|[\Sigma]\right|-[\Sigma]\cdot[\Sigma].$$

This extends the Ozsváth–Szabó adjunction inequality for $\tau$ and the paper's previously established null-homologous case to arbitrary properly embedded surfaces in punctured connected sums of negative complex projective planes. The supplied text does not indicate whether it has been resolved.