Abstract:In our paper, we construct a real-algebraic function on some closed manifold whose Reeb (Kronrod-Reeb) graph is a graph respecting some algebraic domain: a graph for this is called a Poincaré-Reeb graph.The Reeb graph of a smooth function is defined as a natural graph which is the quotient space of the manifold of the domain under a natural equivalence relation for some wide and nice class of smooth functions. The vertex set is defined as the set of all connected components containing some singular points of t… Show more
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