A solvable extended logarithm of the Johnson homomorphism
Takefumi Nosaka
TL;DR
This paper introduces an extension of a logarithmic map related to the Johnson homomorphism, utilizing solvable Lie groups to broaden its domain within the mapping class group of a surface.
Contribution
It presents a novel extension of the Johnson homomorphism's logarithm using solvable Lie groups, expanding its applicability to a larger subset of the mapping class group.
Findings
Extension of the Johnson homomorphism's logarithm to solvable Lie groups.
Broader domain including exponential solvable elements in the mapping class group.
Potential new tools for studying surface mapping class groups.
Abstract
We suggest an extension of a certain logarithm of the total Johnson map in terms of solvable Lie groups. Here, the domain of the map is extended to a subset consisting of exponential solvable elements in the mapping class group of a surface.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory