Notes on the topology of folds

DOI10.2969/jmsj/04430551zbMath0764.57017OpenAlexW2079412159MaRDI QIDQ1201783

Osamu Saeki

Publication date: 17 January 1993

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2969/jmsj/04430551

zbMATH Keywords

Euler numbersmooth mapsfold singular pointsStiefel-Whitney characteristic classes

Mathematics Subject Classification ID

Characteristic classes and numbers in differential topology (57R20) Singularities of differentiable mappings in differential topology (57R45) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25)

Related Items (17)

Elimination of singularities of smooth mappings of 4-manifolds into 3-manifolds ⋮ On holomorphic maps with only fold singularities ⋮ On Reeb graphs induced from smooth functions on 3-dimensional closed manifolds with finitely many singular values ⋮ A remark on elimination of singularities for mappings of 4-manifolds into 3-manifolds. ⋮ Fold maps associated to geodesic random walks on non-positively curved manifolds ⋮ Round fold maps of n-dimensional manifolds into (n-1)-dimensional Euclidean space ⋮ The chess conjecture ⋮ Fold maps on small dimensional manifolds with prescribed singular set ⋮ Immersed 𝑛-manifolds in 𝐑²ⁿ and the double points of their generic projections into 𝐑²ⁿ⁻¹ ⋮ On the vector field problem for \(O(n)/O(1)\times O(1)\times O(n-2)\) ⋮ Self-intersection class for singularities and its application to fold maps ⋮ Classification of singular fibres of stable maps of 4-manifolds into 3-manifolds and its applications ⋮ Remarks on the Topology of Folds ⋮ Characteristic classes and existence of singular maps ⋮ Invariants of fold-maps via stable homotopy groups ⋮ Constructions of round fold maps on smooth bundles ⋮ Fold cobordisms and a Poincaré-Hopf-type theorem for the signature

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