Connected components of strata of Abelian differentials over Teichmüller space

  • Aaron Calderon

    Yale University, New Haven, USA
Connected components of strata of Abelian differentials over Teichmüller space cover

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Abstract

This paper describes connected components of the strata of holomorphic abelian differentials on marked Riemann surfaces with prescribed degrees of zeros. Unlike the case for unmarked Riemann surfaces, we find there can be many connected components, distinguished by roots of the cotangent bundle of the surface. In the course of our investigation we also characterize the images of the fundamental groups of strata inside of the mapping class group. The main techniques of proof are mod winding numbers and a mapping class group–theoretic analogue of the Euclidean algorithm.

Cite this article

Aaron Calderon, Connected components of strata of Abelian differentials over Teichmüller space. Comment. Math. Helv. 95 (2020), no. 2, pp. 361–420

DOI 10.4171/CMH/491