Relative periods of abelian differentials in a prescribed stratum

2025/03/27 by Thomas Le Fils, Fils, Thomas Le
Earth and Planetary Sciences · #Complex Variables (math.CV) #FOS: Mathematics #Geometric Topology (math.GT) #Geophysics and Gravity Measurements

paper · pdf · doi:10.48550/arxiv.2503.21285

openalex publication_date 2025/03/27 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

We characterise the elements of H¹(S, Z, \mathbb C), where S is a closed surface and Z⊂ S is a finite set, that arise as the relative periods of an abelian differential in a given connected component of a stratum of their moduli space. This generalises a theorem obtained independently by Bainbridge, Johnson, Judge and Park and the author, and answers a question of Filip.

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