The geometry and dynamics of twisted quadratic differentials
Name
1117775170-MIT.pdf
Size
11.89 MB
Format
Adobe PDF
Checksum (MD5)
a58064065a34952df53a3e0cbb712880
Author(s)
Wang, Jane,Ph.D.Massachusetts Institute of Technology.
Advisor(s)
Curtis McMullen.
Date Issued
2019
Publisher
Massachusetts Institute of Technology
Abstract
This thesis examines twisted quadratic differentials, also known as dilation surfaces. These are variants of translation surfaces, their more well-studied counterpart. In this work, we study questions about the realizability of mapping class group elements in the affine automorphism groups of dilation surfaces, and how large affine automorphism groups can be. We demonstrate how to construct dilation surfaces with a given pseudo-Anosov map in their affine automorphism group, show the existence of exotic Dehn twists, and construct dilation surfaces with simultaneous Dehn multitwists. The last construction also gives rise to some large affine automorphism groups.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2019
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 91-92).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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