Geodesic
Construction of Transverse Fields
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1146-1159

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we give local conditions for a rectilinear embedding of a non-bounded combinatorial manifold, Mn , in Euclidean space, which are sufficient to prove that Mn has a transverse field (see 1.1 and 1.2, definitions).In a sequel to this paper (6), we will show how with this transverse field we can construct a normal microbundle for the embedded manifold Mn .Our object in this research was only to obtain an existence theorem for normal microbundles. However, the method of proof via the construction of a transverse field yields as corollaries by Cairns (1), Whitehead (9), or Tao (8), results on smoothing. Earlier smoothing results achieved by the construction of transverse fields in the special case of (global) codimension 1 were obtained by Noguchi (5), and Tao (7; 8).After the research for this paper was completed, a paper of Davis (2) came to our attention. 
Putz, H. Construction of Transverse Fields. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1146-1159. doi: 10.4153/CJM-1969-125-6
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