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Abstract
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We give sufficient and necessary conditions for the existence of a fold map of a closed
-dimensional manifold with
prescribed singular set into
for
. To obtain the results
about
-dimensional
manifolds we establish formulas for stable
-framings on
-manifolds by
using symplectic classes. Then we derive conditions about the cobordism classes of oriented
-manifolds which
have fold maps into
.
We also obtain relations between global topological properties of the fold singular set
like the self-intersection number and topological properties of the source manifold like
the Euler characteristic and the signature. We use obstruction theory and the
homotopy principle for fold maps.
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Keywords
singular map, fold map, framing, obstruction, 8-manifold,
signature, symplectic class
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Mathematical Subject Classification
Primary: 57R25, 57R45
Secondary: 55R15, 57R20
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Milestones
Received: 23 September 2021
Revised: 10 September 2022
Accepted: 13 September 2022
Published: 21 March 2023
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Publishers). |
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