A note on subgroups of the Loch Ness Monster Surface's Mapping Class Group
Yannick Krifka, Davide Spriano
TL;DR
This paper provides an elementary proof demonstrating that every countable group can be embedded as a subgroup within the mapping class group of the Loch Ness monster surface, highlighting the group's vast algebraic complexity.
Contribution
It offers a new, elementary proof of the universality of the Loch Ness monster surface's mapping class group for countable groups.
Findings
Every countable group is a subgroup of the mapping class group
Elementary proof approach used for embedding groups
Highlights the algebraic richness of the surface's mapping class group
Abstract
In this short note we give an elementary proof of the fact that every countable group is a subgroup of the mapping class group of the Loch Ness monster surface.
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Taxonomy
TopicsGeometric and Algebraic Topology · Computational Geometry and Mesh Generation · Mathematical Dynamics and Fractals