#### Volume 21, issue 4 (2021)

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Configurations of noncollinear points in the projective plane

### Ronno Das and Ben O’Connor

Algebraic & Geometric Topology 21 (2021) 1941–1972
##### Abstract

We consider the space ${F}_{n}$ of configurations of $n$ points in ${ℙ}^{2}$ satisfying the condition that no three of the points lie on a line. For $n=4,5,6$, we compute ${H}^{\ast }\left({F}_{n};ℚ\right)$ as an ${\mathfrak{𝔖}}_{n}$–representation. The cases $n=5,6$ are computed via the Grothendieck–Lefschetz trace formula in étale cohomology and certain “twisted” point counts for analogous spaces over ${\mathbb{𝔽}}_{\phantom{\rule{-0.17em}{0ex}}q}$.

##### Keywords
collinear, configuration space, cohomology, projective plane, hyperplane complement
##### Mathematical Subject Classification 2010
Primary: 55R80
Secondary: 14F25, 14J10