Translation Surfaces: 242 (Graduate Studies in Mathematics) - Softcover

Jayadev S. Athreya (author) & Howard Masur (author)

Softcover

ISBN 10: 1470476770 ISBN 13: 9781470476779

Publisher: American Mathematical Society, 2024

Synopsis

This textbook offers an accessible introduction to translation surfaces. Building on modest prerequisites, the authors focus on the fundamentals behind big ideas in the field: ergodic properties of translation flows, counting problems for saddle connections, and associated renormalization techniques. Proofs that go beyond the introductory nature of the book are deftly omitted, allowing readers to develop essential tools and motivation before delving into the literature. Beginning with the fundamental example of the flat torus, the book goes on to establish the three equivalent definitions of translation surface. An introduction to the moduli space of translation surfaces follows, leading into a study of the dynamics and ergodic theory associated to a translation surface. Counting problems and group actions come to the fore in the latter chapters, giving a broad overview of progress in the 40 years since the ergodicity of the Teichmuller geodesic flow was proven. Exercises are included throughout, inviting readers to actively explore and extend the theory along the way. Translation Surfaces invites readers into this exciting area, providing an accessible entry point from the perspectives of dynamics, ergodicity, and measure theory. Suitable for a one- or two-semester graduate course, it assumes a background in complex analysis, measure theory, and manifolds, while some familiarity with Riemann surfaces and ergodic theory would be beneficial.

About this title

About the Author

Jayadev S. Athreya, University of Washington, Seattle, WA.

Howard Masur, University of Chicago, IL.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2024
• Language: English
• ISBN 10: 1470476770
• ISBN 13: 9781470476779
• Binding: Paperback
• Number of pages: 277