%0 Generic %1 taylor1998smooth %A Taylor, Laurence R. %D 1998 %K 4-spaces euclidean smooth %T Smooth Euclidean 4-spaces with few symmetries %U http://arxiv.org/abs/math/9807143 %X 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, S^1 can not act smoothly and effectively on any smoothing of 4-space with barrier 3-spheres.

@misc{taylor1998smooth, 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.}, added-at = {2013-12-23T04:26:50.000+0100}, author = {Taylor, Laurence R.}, biburl = {https://www.bibsonomy.org/bibtex/2c2b18a2543a703e46e228094300bc07d/aeu_research}, description = {Smooth Euclidean 4-spaces with few symmetries}, interhash = {29df3f151fc68d1e00ef25b9ef8077f8}, intrahash = {c2b18a2543a703e46e228094300bc07d}, keywords = {4-spaces euclidean smooth}, note = {cite arxiv:math/9807143Comment: 7 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper26.abs.html}, timestamp = {2013-12-23T04:37:02.000+0100}, title = {Smooth Euclidean 4-spaces with few symmetries}, url = {http://arxiv.org/abs/math/9807143}, year = 1998 }