A representation theoretic approach to the mapping class group of surfaces

2017 Fiscal Year Final Research Report

• Project/Area Number: 26870368
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry; Algebra
• Research Institution: The University of Electro-Communications
• Principal Investigator: Enomoto Naoya 電気通信大学, 大学院情報理工学研究科, 准教授 (50565710)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 写像類群 / 表現論 / Johnson準同型

Outline of Final Research Achievements

The Johnson hoomorphism for the mapping class group of surfaces give an approximation for the Torelli subgroup of the mapping class group in the Lie algebra of the symplectic derivations. In this study, we evaluate the Johnson image in the Lie algebra of symplectic derivations.
First, we give a new class (Enomoto-Satoh obstruction) in the cokernel of the Johnson homomorphism using the structure of the Johnson cokernels for the IA-automorphism group for the free group. Second, we detect some new series ("anti-Morita" obstructions and some "hook type obstruction" )of Sp-irreducible representations in the Johnson cokernels for the mapping class group. Our results suggest that the Johnson image is not so big in the Lie algebra of symplectic derivations.

Free Research Field

表現論