For closed manifolds obtained by mixing two spheres and a real curve, the paper classifies the critical sets of the height function and of its newly introduced first-derivative function.
Regions represented as foliated forms and natural smooth maps onto them
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
The author is interested in regions surrounded by hypersurfaces and natural smooth maps onto them respecting the canonical projections of the unit spheres and so-called special generic maps and moment maps, more generally. We consider situations where these regions are foliated via 1-dimensional families of functions and their zero sets (smoothly). We including the author are also interested in explicit and nice functions obtained by composing the canonical projections and their topological or combinatorial properties. This is of singularity theory of differentiable maps and applications to differential topology and various real geometry. Explicitly, here, as a new challenge, we discuss the 1st derivative of such a function and critical sets of this.
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math.DG 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
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Fundamental examples of height functions on closed manifolds and their 1st derivatives
For closed manifolds obtained by mixing two spheres and a real curve, the paper classifies the critical sets of the height function and of its newly introduced first-derivative function.