Teichmuller theory and collapse of flat manifolds

Author(s)

Bettiol, Renato G. ^[1] ; Derdzinski, Andrzej ^[2] ; Piccione, Paolo ^[3]

Affiliation

^[1] Univ Penn, Dept Math, 209 South 33rd St, Philadelphia, PA 19104 - USA

^[2] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 - USA

^[3] Univ Sao Paulo, Dept Matemat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: Annali di Matematica Pura ed Applicata; v. 197, n. 4, p. 1247-1268, AUG 2018.
• Web of Science Citations: 1

Abstract

We provide an algebraic description of the Teichmuller space and moduli space of flat metrics on a closed manifold or orbifold and study its boundary, which consists of (isometry classes of) flat orbifolds to which the original object may collapse. It is also shown that every closed flat orbifold can be obtained by collapsing closed flat manifolds, and the collapsed limits of closed flat 3-manifolds are classified. (AU)

• FAPESP's process: 15/50315-3 - Geometry and Dynamics between Ohio and São Paulo
• Grantee: Paolo Piccione
• Support Opportunities: Regular Research Grants