Abstract
In this chapter we construct a cellular decomposition of Teichmüller space. The construction is based on the hyperbolic geometry of a Riemann surface, which we review in Sections 5 and 6. The cells of the decomposition are labelled by ribbon graphs, and the decomposition itself is equivariant under the action of the Teichmüller modular group. We then extend this decomposition to the bordification of Teichmüller space introduced in Chapter XV. By equivariance, this provides orbicellular decompositions of the moduli spaces of pointed Riemann surfaces and of suitable compactifications.
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© 2011 Springer-Verlag Berlin Heidelberg
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Arbarello, E., Cornalba, M., Griffiths, P.A. (2011). Cellular decomposition of moduli spaces. In: Geometry of Algebraic Curves. Grundlehren der mathematischen Wissenschaften, vol 268. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69392-5_10
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DOI: https://doi.org/10.1007/978-3-540-69392-5_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42688-2
Online ISBN: 978-3-540-69392-5
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