
TL;DR
This paper investigates the stability of maps, focusing on their automorphisms and how they relate to their orientable double covers, revealing new families of unstable maps and connections to other mathematical structures.
Contribution
It introduces several infinite families of unstable maps and explores their relationships with graphs, hypermaps, and Klein surfaces.
Findings
Identification of infinite families of unstable maps
Relationship between unstable maps and automorphisms of their double covers
Connections to similar phenomena in graphs, hypermaps, and Klein surfaces
Abstract
A map which is non-orientable or has non-empty boundary has a canonical double cover which is orientable and has empty boundary. The map is called stable if every automorphism of this cover is a lift of an automorphism of the map. This note describes several infinite families of unstable maps, and relates them to similar phenomena for graphs, hypermaps and Klein surfaces.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows
