Square Tiled Surfaces and Teichmüller Volumes of the Moduli Spaces of Abelian Differentials

Anton Zorich ()
Additional contact information
Anton Zorich: Université de Rennes 1, Institut de recherche mathématique de Rennes

A chapter in Rigidity in Dynamics and Geometry, 2002, pp 459-471 from Springer

Abstract: Abstract We present an approach for counting the Teichmüller volumes of the moduli spaces of Abelian differentials on a Riemann surface of genus g. We show that the volumes can be counted by means of counting the “integer points” in the corresponding moduli space. The “integer points” are represented by square tiled surfaces — the flat surfaces tiled by unit squares. Such tilings have several conical singularities with 8, 12,... adjacent unit squares. Counting the leading term in the asymptotics of the number of tilings having at most N unit squares, we get the volumes of the corresponding strata of the moduli spaces.

Keywords: Modulus Space; Riemann Surface; Lyapunov Exponent; Boundary Component; Integer Point (search for similar items in EconPapers)
Date: 2002
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04743-9_25

Ordering information: This item can be ordered from
http://www.springer.com/9783662047439

DOI: 10.1007/978-3-662-04743-9_25

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().