Desingularizing maps of corank one

S. J. Blank, C. Curley
1980 Proceedings of the American Mathematical Society  
In 1960, A. Haefliger presented necessary and sufficient conditions for factoring a smooth map from a surface into the plane through an immersion into R3. Here, necessary and sufficient conditions are given for factoring a map between manifolds of dimension n, n > 2, through an immersion into a line bundle over the range. In addition, conditions are given for factoring such a map through a submersion from a line bundle over the domain.
doi:10.1090/s0002-9939-1980-0581010-8 fatcat:m37b3ukupnelhn66m2yb4j3rya