Surgery along star shaped plumbings and exotic smooth structures on 4-manifolds
Geometric Topology
2016-07-20 v3 Symplectic Geometry
Abstract
We define a new 4-dimensional symplectic cut and paste operation which is analogous to Fintushel and Stern's rational blow-down. We use this operation to produce multiple constructions of symplectic smoothly exotic complex projective space blown-up eight times, seven times, and six times. We also show how this operation can be used in conjunction with knot surgery to construct an infinite family of minimal exotic smooth structures on the complex projective space blown-up seven times.
Keywords
Cite
@article{arxiv.1402.0801,
title = {Surgery along star shaped plumbings and exotic smooth structures on 4-manifolds},
author = {Cagri Karakurt and Laura Starkston},
journal= {arXiv preprint arXiv:1402.0801},
year = {2016}
}
Comments
35 pages, 20 figures; v2 has significantly more examples of small exotic symplectic 4-manifolds including exotic CP2 blown up 6 and 7 times and the structure of the paper is reorganized; v3 corrects minor errors and some inconsistencies in conventions