On the singularities of foliations and of vector bundle maps |
| |
Authors: | Bruce F. Golbus |
| |
Affiliation: | (1) Wayne State University, Detroit, Michigan |
| |
Abstract: | LetF be a (smooth) Γ q ∞ -stucture (often called a codimension-q Haefliger structure) on a compact manifoldX n . Cohomological invariants associated to the singularities ofF are defined whose vanishing is shown to be a necessary condition for deformingF to a codimension-q foliation onX n . An analagous approach to vector bundle maps is then utilized to prove a general theorem concerning the possibility of embedding a vector bundle in the tangent bundle ofX n , and applications to the planefield problem are given. In the final section geometric realizations of the singularity classes associated toF are constructed. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|