The focused study of automorphism groups of free groups and the mapping class groups for the Johnson homomorphisms

2015 Fiscal Year Final Research Report

• Project/Area Number: 24740051
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Tokyo University of Science
• Principal Investigator: Satoh Takao 東京理科大学, 理学部, 准教授 (70533256)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 自由群の自己同型群 / Johnson準同型 / 群のコホモロジー / 写像類群

Outline of Final Research Achievements

We obtained many new results for the Andreadakis-Johnson filtration and the Johnson homomorphisms of the automrophism groups of free groups. In particular, we gave the affirmative answer to the Andreadakis conjecture for the upper triangular automorphism groups, and established an analogue of the Johnson-Morita theory by using the rings of Fricke characters of free groups and the rings of SL(m,C)-representations of free groups. We expect that these results have good applications for the study of the mapping class groups of surfaces.

Free Research Field

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