On the unit component of the Newman-Unti group
Alexander Schmeding
TL;DR
This paper identifies the unit component of the Newman-Unti group within a specific topology and clarifies its Lie group structure, contrasting it with the full group's properties.
Contribution
It precisely characterizes the unit component of the NU group and establishes its infinite-dimensional Lie group structure, unlike the full group.
Findings
The unit component of the NU group is identified within the fine very strong topology.
The unit component admits an infinite-dimensional Lie group structure.
The full NU group does not support a Lie group structure.
Abstract
In this short note we identify the unit component of the Newman--Unti (NU) group in the fine very strong topology. In previous work, this component has been endowed with an infinite-dimensional Lie group structure, while the full NU-group does not support such a structure.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models