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Smooth Euclidean 4–spaces with few symmetries

Laurence R Taylor

Geometry & Topology Monographs 2 (1999) 563–569

DOI: 10.2140/gtm.1999.2.563

arXiv: math.GT/9807143

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. The existence of barriers implies, amongst other things, that the isometry group of these manifolds, in any smooth metric, is finite. In particular, S1 can not act smoothly and effectively on any smoothing of 4–space with barrier 3–spheres.

Keywords

exotic smoothings, Euclidean spaces, isometries

Mathematical Subject Classification

Primary: 57R55

References
Publication

Received: 28 July 1998
Published: 21 November 1999

Authors
Laurence R Taylor
Department of Mathematics
University of Notre Dame
Notre Dame IN 46556
USA