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CAT(0) geometry of complex curve complements and families

Kejia Zhu ⟨kzhumath@gmail.com⟩

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 P2, we show that π1(P2C) is CAT(0). In the other direction, we prove that the fundamental group of the universal family associated with the singularities of type E6, E7, and E8 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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