Mapping Class Groups do not have Kazhdan's Property (T)
Jorgen Ellegaard Andersen
TL;DR
This paper proves that the mapping class group of a closed oriented surface of genus at least two does not possess Kazhdan's Property (T), clarifying its representation-theoretic properties.
Contribution
It establishes the non-existence of Kazhdan's Property (T) for a broad class of mapping class groups, a significant result in geometric group theory.
Findings
Mapping class groups lack Kazhdan's Property (T)
Implications for representation theory of these groups
Advances understanding of geometric group properties
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).
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology