Every tree, and certain graphs assembled from single edges and small circles, is the Reeb graph of a Morse-Bott real algebraic function defined by degree-1 and degree-2 polynomials.
The masterpieces of John Forbes Nash Jr
1 Pith paper cite this work. Polarity classification is still indexing.
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In this note I have tried to rewrite four famous works of Nash in a more modern language while adhering as much as possible to the original arguments.
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Graphs with tree decompositions of small graphs and realizing them as the Reeb graphs of real algebraic functions
Every tree, and certain graphs assembled from single edges and small circles, is the Reeb graph of a Morse-Bott real algebraic function defined by degree-1 and degree-2 polynomials.