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Construction of Transverse Fields

Published online by Cambridge University Press:  20 November 2018

H. Putz
H. Putz*
Affiliation:
Temple University, Philadelphia, Pennsylvania
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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.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969, pp. 1146 - 1159
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Cairns, S. S., Homeomorphisms between topological manifolds and analytic manifolds, Ann. of Math. (2) 41 (1940), 796–808.Google Scholar
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