Smooth Euclidean 4-spaces with few symmetries

Laurence R. Taylor

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arXiv · math/9807143

Smooth Euclidean 4-spaces with few symmetries

Laurence R. Taylor

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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.

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BibTeX RIS

Laurence R. Taylor. 1999-11-21. Smooth Euclidean 4-spaces with few symmetries. https://arxiv.org/abs/math/9807143

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