Sections of Serre fibrations with low-dimensional fibers

Details Sections of Serre fibrations with low-dimensional fibers Sections of Serre fibrations with low-dimensional fibers

2002-08-24

arxiv.org/abs/math/0208192v1

Mathematics

Geometric Topology

22 pages

Scientific paper

It was proved by H. Whitney in 1933 that it is possible to mark a point in all curves in a continuous way. The main result of this paper extends the Whitney theorem to dimensions 2 and 3. Namely, we prove that it is possible to choose a point continuously in all two-dimensional surfaces sufficiently close to a given surface, and in all 3-manifolds sufficiently close to a given 3-manifold.

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