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- Title
IMMERSIONS AND TRANSLATION STRUCTURES I: THE SPACE OF STRUCTURES ON THE POINTED DISK.
- Authors
HOOPER, W. PATRICK
- Abstract
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.
- Subjects
MODULI theory; IMMERSIONS (Mathematics); TOPOLOGY; ISOMORPHISM (Mathematics); HAUSDORFF spaces
- Publication
Conformal Geometry & Dynamics, 2018, Vol 22, Issue 11, p235
- ISSN
1088-4173
- Publication type
Article
- DOI
10.1090/ecgd/326