A comparison of classes in the Johnson cokernels of the mapping class groups of surfaces

Naoya Enomoto, Yusuke Kuno, Takao Satoh

Research output: Contribution to journalArticle

Abstract

In [8], the first and the third authors introduced new classes in the Johnson cokernels of the mapping class groups of surfaces by a representation theoretic approach based on some previous results for the Johnson cokernels of the automorphism groups of free groups. On the other hand, in [15], Kawazumi and the second author introduced another type of classes by a topological consideration of self-intersections of curves on a surface. In this paper, we show that the classes found in [15] are contained in the classes found in [8] in a stable range. Furthermore, we prove that the anti-Morita obstructions [14m+1] for m≥1 obtained in [8] and a hook-type component [3,15] detected in [6] appear in their gap.

Original languageEnglish
Article number107052
JournalTopology and its Applications
Volume271
DOIs
Publication statusPublished - 15 Feb 2020

Keywords

  • Johnson homomorphism
  • Mapping class groups

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