Characteristic classes of moduli spaces— Riemann surface, graph, homology cobordism

Morita, Shigeyuki

doi:10.1090/suga/453

Cited by 1 publication

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“…As explained in Section 10, such a decomposition corresponds to an Ihara curve and thus determines an action of the motivic Lie algebra mtm on p(S, v). Morita [66] has proposed a location of the image of the generator σ 2n+1 of k in Gr W −4n−2 Der θ p(S, v). Here we discuss Morita's proposal.…”

Section: Remarks On a Conjecture Of Moritamentioning

confidence: 99%

Johnson Homomorphisms

Hain

2019

Preprint

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Torelli groups are subgroups of mapping class groups that consist of those diffeomorphism classes that act trivially on the homology of the associated closed surface. The Johnson homomorphism, defined by Dennis Johnson, and its generalization, defined by S. Morita, are tools for understanding Torelli groups. This paper surveys work on generalized Johnson homomorphisms and tools for studying them. The goal is to unite several related threads in the literature and to clarify existing results and relationships among them using Hodge theory. We survey the work of Alekseev, Kawazumi, Kuno and Naef on the Goldman-Turaev Lie bialgebra, and the work of various authors on cohomological methods for determining the stable image of generalized Johnson homomorphisms. Various open problems and conjectures are included.Even though the Johnson homomorphisms were originally defined and studied by topologists, they are important in understanding arithmetic properties of mapping class groups and moduli spaces of curves. We define arithmetic Johnson homomorphisms, which extend the generalized Johnson homomorphisms, and explain how the Turaev cobracket constrains their images.

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Section: Remarks On a Conjecture Of Moritamentioning

confidence: 99%

Johnson Homomorphisms

Hain

2019

Preprint

View full text Add to dashboard Cite

show abstract

Characteristic classes of moduli spaces— Riemann surface, graph, homology cobordism

Cited by 1 publication

References 83 publications

Johnson Homomorphisms

Johnson Homomorphisms

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