Abstract
Fintushel-Stern's knot surgery has given many exotic 4-manifolds. We show that if an elliptic fibration has two, parallel, oppositely-oriented vanishing cycles (for example $S^2\times S^2$ or Matsumoto's $S^4$), then the knot surgery does not change its differential structure. We also give a classification of link surgery of $S^2\times S^2$ and a generalization of Akbulut's celebrated result that Scharlemann's manifold is standard.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
