Vol. 34, No. 2, 1970

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Fibrations of analytic varieties

Keith Milo Kendig

Vol. 34 (1970), No. 2, 441–451

The induced continuous, differentiable, or analytic fibering about any point of a continuous, differentiable, or analytic group A, by a subgroup B is well known, as are generalizations to various spaces with operators. One may ask about analogous results for varieties per se. For instance, if C is any arc in E2 and p C, then there is always a homeomorphism φ from a neighborhood U of p to I × I(I = (0,1)), so that φ(U C) = I ×{1
2}. But there are arcs in Es which are so wildly embedded that at no point of the arc is there an analogous fibering. This paper considers a general fibration problem for complexanalytic varieties, and extends a result on fibering hypersurfaces due to Hassler Whitney.

Mathematical Subject Classification
Primary: 32.44
Received: 4 June 1969
Published: 1 August 1970
Keith Milo Kendig