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arXiv · 2005.02606

Degree 2 Transformation Semigroups as Continuous Maps on Graphs: Foundations and Structure

Stuart W. Margolis·John Rhodes
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Abstract

We develop the theory of transformation semigroups that have degree 2, that is, act by partial functions on a finite set such that the inverse image of points have at most two elements. We show that the graph of fibers of such an action gives a deep connection between semigroup theory and graph theory. It is known that the Krohn-Rhodes complexity of a degree 2 action is at most 2. We show that the monoid of continuous maps on a graph is the translational hull of an appropriate 0-simple semigroup. We show how group mapping semigroups can be considered as regular covers of their right letter mapping image and relate this to their graph of fibers.

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Stuart W. Margolis, John Rhodes. 2020-05-06. Degree 2 Transformation Semigroups as Continuous Maps on Graphs: Foundations and Structure. https://arxiv.org/abs/2005.02606

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