Geometry & Topology Monographs 2 (1999),
Proceedings of the Kirbyfest,
paper no. 26, pages 563-569.
Smooth Euclidean 4-spaces with few symmetries
Laurence R Taylor
Abstract.
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.
Keywords.
Exotic smoothings, Euclidean spaces, isometries
AMS subject classification.
Primary: 57R55.
E-print: arXiv:math.GT/9807143
Submitted: 28 July 1998.
Published: 21 November 1999.
Notes on file formats
Laurence R Taylor
Department of Mathematics, University of Notre Dame
Notre Dame, IN 46556, USA
Email: taylor.2@nd.edu
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