Mapping Class Groups do not have Kazhdan's Property (T)

Abstract

We prove that the mapping class group of a closed oriented surface of genus at least two does not have Kazhdan's property (T).

References in corpus (7)

• Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to \infty$
• Geometric construction of modular functors from Conformal Field Theory
• Abelian Conformal Field theories and Determinant Bundles
• Hitchin's connection, Toeplitz operators and symmetry invariant deformation quantization
• Modular functors are determined by their genus zero data
• Some asymptotics of TQFT via skein theory
• Irreducibility of some quantum representations of mapping class groups

Cited by in corpus (16)

• Groups acting on manifolds: around the Zimmer program
• A survey of Measured Group Theory
• Median structures on asymptotic cones and homomorphisms into mapping class groups
• Abelian quotients of subgroups of the mapping class group and higher Prym representations
• Construction of the Witten-Reshetikhin-Turaev TQFT from conformal field theory
• Hitchin's Projectively Flat Connection, Toeplitz Operators and the Asymptotic Expansion of TQFT Curve Operators
• Hitchin's connection, Toeplitz operators and symmetry invariant deformation quantization
• Hitchin's Connection in Half-Form Quantization
• Group actions on median spaces
• Mapping class group invariant unitarity of the Hitchin connection over Teichmüller space
• A geometric formula for the Witten-Reshetikhin-Turaev Quantum Invariants and some applications
• Cohomology of mapping class groups and the abelian moduli space
• Property $(TT)$ modulo $T$ and homomorphism superrigidity into mapping class groups
• On Reducibility of Mapping Class Group Representations: The SU(N) Case
• Hitchin connection on the Veech curve
• Reducibility of quantum representations of mapping class groups