Toric cubes are closed balls
Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov
TL;DR
Toric cubes, formed by monomial maps from unit cubes, are shown to be topologically equivalent to closed balls, revealing their geometric and algebraic structure.
Contribution
The paper demonstrates that toric cubes are the closures of graphs of monotone maps and are semi-algebraically homeomorphic to closed balls, establishing their topological nature.
Findings
Toric cubes are closures of graphs of monotone maps.
Toric cubes are semi-algebraically homeomorphic to closed balls.
Toric cubes are images of [0,1]^d under monomial maps.
Abstract
We prove that toric cubes, which are images of under monomial maps, are the closures of graphs of monotone maps, and in particular semi-algebraically homeomorphic to closed balls.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Mathematical Dynamics and Fractals · Geometric and Algebraic Topology