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arXiv · 2408.17301

Integral cohomology of dual boundary complexes is motivic

Tao Su
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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 stably affine space (of positive dimension) is contractible. In a separate paper [Su23], this corollary has been used by the author in his proof of the weak geometric P=W conjecture for very generic $GL_n(\mathbb{C})$-character varieties over any punctured Riemann surfaces.

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Tao Su. 2024-08-30. Integral cohomology of dual boundary complexes is motivic. https://arxiv.org/abs/2408.17301

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