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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Immersions and translation structures I: The space of structures on the pointed disk
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by W. Patrick Hooper PDF
Conform. Geom. Dyn. 22 (2018), 235-270


We define a moduli space of translation structures on the open topological disk with a basepoint and endow it with a locally-compact metrizable topology. We call this the immersive topology, because it is defined using the concept of immersions: continuous maps between subsets of translation surfaces that respect the basepoints and the translation structures. Immersions induce a partial ordering on the moduli space, and we prove the ordering is nearly a complete lattice in the sense of order theory; the space is only missing a minimal element. Subsequent articles will uncover more structure and develop a topology on the space of all translation structures.
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Additional Information
  • W. Patrick Hooper
  • Affiliation: Department of Mathematics, The City College of New York, New York, New York, 10031
  • MR Author ID: 759028
  • Email:
  • Received by editor(s): May 29, 2014
  • Received by editor(s) in revised form: June 2, 2015, May 27, 2016, and August 7, 2018
  • Published electronically: October 23, 2018
  • Additional Notes: Support was provided by N.S.F. Grants DMS-1101233 and DMS-1500965 as well as a PSC-CUNY Award (funded by The Professional Staff Congress and The City University of New York).
  • © Copyright 2018 W. Patrick Hooper
  • Journal: Conform. Geom. Dyn. 22 (2018), 235-270
  • MSC (2010): Primary 57M50; Secondary 30F30, 32G15, 37E99, 06B23
  • DOI:
  • MathSciNet review: 3867283