Obstructions to the existence of fold maps

Rustam Sadykov, Osamu Saeki, Kazuhiro Sakuma

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We study smooth maps between smooth manifolds with only fold points as their singularities, and clarify the obstructions to the existence of such a map in a given homotopy class for certain dimensions. The obstructions are described in terms of characteristic classes, which arise as Postnikov invariants, and can be interpreted as primary and secondary obstructions to the elimination of certain singularities. We also discuss the relationship between the existence problem of fold maps and that of vector fields of stabilized tangent bundles.

Original languageEnglish
Pages (from-to)338-354
Number of pages17
JournalJournal of the London Mathematical Society
Volume81
Issue number2
DOIs
Publication statusPublished - Apr 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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