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March 2014 The link surgery of $S^2\times S^2$ and Scharlemann's manifolds
Motoo Tange
Hiroshima Math. J. 44(1): 35-62 (March 2014). DOI: 10.32917/hmj/1395061556

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.

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Motoo Tange. "The link surgery of $S^2\times S^2$ and Scharlemann's manifolds." Hiroshima Math. J. 44 (1) 35 - 62, March 2014. https://doi.org/10.32917/hmj/1395061556

Information

Published: March 2014
First available in Project Euclid: 17 March 2014

zbMATH: 1317.57020
MathSciNet: MR3178435
Digital Object Identifier: 10.32917/hmj/1395061556

Subjects:
Primary: 57R65 , 98B76
Secondary: 57M25 , 57R50

Keywords: Fintushel-Stern's knot surgery , Kirby calculus , Scharlemann manifolds

Rights: Copyright © 2014 Hiroshima University, Mathematics Program

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Vol.44 • No. 1 • March 2014
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