Moduli spaces of complex affine and dilation surfaces

DOI10.1515/crelle-2023-0005OpenAlexW4321494868MaRDI QIDQ2689044

Matt Bainbridge, Jane Wang, Paul Apisa

Publication date: 6 March 2023

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.05257

Mathematics Subject Classification ID

Algebraic geometry (14-XX) Several complex variables and analytic spaces (32-XX)

Cites Work

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• Les surfaces euclidiennes à singularités coniques. (Euclidean surfaces with cone singularities)
• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Monodromy of hypergeometric functions and non-lattice integral monodromy
• Dilation surfaces and their Veech groups
• Angels' staircases, Sturmian sequences, and trajectories on homothety surfaces
• Connected components of the strata of the moduli space of meromorphic differentials
• Teichmüller dynamics, dilation tori and piecewise affine circle homeomorphisms
• Homology of the moduli spaces and mapping class groups of framed, r -Spin and Pin surfaces
• Cascades in the dynamics of affine interval exchange transformations
• Spin Structures and Quadratic forms on Surfaces
• Flat Surfaces
• The mapping class group orbits in the framings of compact surfaces
• The Realization Problem for Dilation Surfaces
• Horizon saddle connections and Morse-Smale dynamics of dilation surfaces

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