Celebratio Mathematica — Kister — Complete Bibliography

Complete Bibliography

Works connected to Raymond Louis Wilder

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J. M. Kister: “Inverses of Euclidean bundles,” Mich. Math. J. 14 : 3 (1967), pp. 349–352. To Raymond L. Wilder on his seventieth birthday. MR 212830 Zbl 0149.40903 article

For each Euclidean bundle or microbundle it is useful to find another bundle of the same type, called an inverse bundle, such that the Whitney sum of the two is a trivial bundle. Milnor in [4] ingeniously showed how to construct an inverse to a microbundle over a finite-dimensional, locally finite, simplicial complex. Here we give a short and elementary proof of the existence of inverses for Euclidean bundles over paracompact spaces having a finiteness condition. This contains Milnor’s result, since one may regard a microbundle as a Euclidean bundle [2]. Hirsch [1] has also developed a new proof of the existence of the inverse of a bundle over a polyhedron, in his work on the stable existence and stable isotopy of normal microbundles.