Integral cohomology of dual boundary complexes is motivic

Abstract

In this note, we give a motivic characterization of the integral cohomology of dual boundary complexes of smooth quasi-projective complex algebraic varieties. As a corollary, the dual boundary complex of any variety stably isomorphic to ${\mathbb{G}}_m^r\times {\mathbb{A}}^s$ with $s>0$ is contractible. In a separate paper [Su26], this corollary has been used by the author in his proof of the weak geometric P=W conjecture for very generic $G{L}_n(\mathbb{C})$-character varieties over any punctured Riemann surfaces.

arXiv commentv2: 8 pages; minor revision