Constructing Group-Invariant CR Mappings
Jennifer Brooks, Sean Curry, Dusty Grundmeier, Purvi Gupta, Valentin, Kunz, Alekzander Malcom, Kevin Palencia
TL;DR
This paper develops new methods for constructing group-invariant CR mappings between spheres, combining tensoring techniques with existing canonical mappings, and investigates potential gaps in the invariant mapping space.
Contribution
It introduces a novel combination of tensoring and canonical construction methods to generate new invariant CR mappings and explores gap phenomena in this context.
Findings
New invariant CR mappings constructed using combined methods
Identification of potential gap phenomena in invariant mappings
Extension of canonical group-invariant CR mapping techniques
Abstract
We construct CR mappings between spheres that are invariant under actions of finite unitary groups. In particular, we combine a tensoring procedure with D'Angelo's construction of a canonical group-invariant CR mapping to obtain new invariant mappings. We also explore possible gap phenomena in this setting.
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Taxonomy
TopicsHolomorphic and Operator Theory · Geometric and Algebraic Topology · Advanced Topics in Algebra