Smooth Euclidean 4-spaces with few symmetries

Details Smooth Euclidean 4-spaces with few symmetries Smooth Euclidean 4-spaces with few symmetries

1998-07-26

arxiv.org/abs/math/9807143v2

Geom. Topol. Monogr. 2 (1999), 563-569

Mathematics

Geometric Topology

7 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper26.abs.html

Scientific paper

We say that a topologically embedded 3-sphere in a smoothing of Euclidean 4-space is a barrier provided, roughly, no diffeomorphism of the 4-manifold moves the 3-sphere off itself. In this paper we construct infinitely many one parameter families of distinct smoothings of 4-space with barrier 3-spheres. \par The existence of barriers implies, amongst other things, that the isometry group of these manifolds, in any smooth metric, is finite. In particular, S^1 can not act smoothly and effectively on any smoothing of 4-space with barrier 3-spheres.

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