Fold maps, framed immersions and smooth structures

DOI10.1090/S0002-9947-2011-05485-1zbMath1244.57054arXiv0803.3780WikidataQ125863968 ScholiaQ125863968MaRDI QIDQ5389423

Rustam Sadykov

Publication date: 26 April 2012

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

Full work available at URL: https://arxiv.org/abs/0803.3780

zbMATH Keywords

stable vector bundlefold mapfold singular pointreduced cobordism class of a fold mapspectrum of a cobordism theory

Mathematics Subject Classification ID

Bordism and cobordism theories and formal group laws in algebraic topology (55N22) Singularities of differentiable mappings in differential topology (57R45)

Related Items

Fold maps, framed immersions and smooth structures ⋮ Fold cobordisms and a Poincaré-Hopf-type theorem for the signature

Cites Work

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• The stability theorem for smooth pseudoisotopies
• The homotopy type of the cobordism category
• Madsen-Weiss for geometrically minded topologists
• Cobordism of singular maps
• Cobordisms of maps with singularities of given class
• Fold maps and immersions from the viewpoint of cobordism
• Bordism groups of solutions to differential relations
• Vector fields and other vector bundle morphisms - a singularity approach
• Quillenization and bordisms
• Wrinkling of smooth mappings. III. Foliations of codimension greater than one
• Pontrjagin-Thom-type construction for maps with singularities
• On special generic maps into \(\mathbb{R}^3\)
• Invariants of fold-maps via stable homotopy groups
• The stable moduli space of Riemann surfaces: Mumford's conjecture
• Singular fibers and characteristic classes
• Singularities of differentiable maps
• Cobordism invariants of fold maps
• Obstructions to the existence of fold maps
• A Second note on Symmetry of Singularities
• Remarks on the Topology of Folds
• Self-intersection class for singularities and its application to fold maps
• Bordism groups of special generic mappings
• Fold maps, framed immersions and smooth structures
• Cobordism groups of immersions
• Symmetry properties of singularities of \(C^\infty\)-functions