Abstract:
Motivated by the question of whether braid groups are CAT(0), we investigate the CAT(0) behavior of fundamental groups of plane curve complements and certain universal families. If $C$ is the branch locus of a generic projection of a smooth, complete intersection surface to $\mathbb{P}^2$, we show that $\pi_1(\mathbb{P}^2\setminus C)$ is CAT(0). In the other direction, we prove that the fundamental group of the universal family associated with the singularities of type $E_6$, $E_7$, and $E_8$ is not CAT(0). Other examples, both positive and negative, are discussed, with a special emphasis on rational 3-cuspidal curves. This is joint work with C. Bregman and A. Libgober.
Scheduled for: 2025-03-08 10:20 AM: Kejia Zhu (virtual) in Forbes 2070E
Status: Accepted
Collection: Geometric Group Theory
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