Connected components of strata of Abelian differentials over\n Teichm "uller space

2019/01/16 by Aaron J. Calderon, Calderon, Aaron
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Analytic and geometric function theory #FOS: Mathematics #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.1901.05482

openalex publication_date 2019/01/16 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28

Abstract

This paper describes connected components of the strata of holomorphic\nabelian differentials on marked Riemann surfaces with prescribed degrees of\nzeros. Unlike the case for unmarked Riemann surfaces, we find there can be many\nconnected components, distinguished by roots of the cotangent bundle of the\nsurface. In the course of our investigation we also characterize the images of\nthe fundamental groups of strata inside of the mapping class group. The main\ntechniques of proof are mod r winding numbers and a mapping class\ngroup-theoretic analogue of the Euclidean algorithm.\n

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