Special generic maps and Gromoll filtration
Osamu Saeki

TL;DR
This paper explores the relationship between special generic maps of homotopy spheres into Euclidean spaces and the Gromoll filtration, establishing a precise equivalence for spheres of dimension at least six.
Contribution
It characterizes when homotopy spheres admit special generic maps into Euclidean spaces based on their Gromoll filtration, linking differential topology and geometric mapping properties.
Findings
Homotopy spheres admit special generic maps iff their Gromoll filtration equals the target dimension.
The result holds for spheres of dimension at least six.
Provides a new criterion connecting Gromoll filtration to the existence of special generic maps.
Abstract
A smooth map of a closed -dimensional manifold into with is a special generic map if it has only definite folds as its singularities. We show that for and , a homotopy -sphere admits a special generic map into with standard properties if and only if its Gromoll filtration is equal to .
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis · Advanced Combinatorial Mathematics
