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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On $3$-manifolds that are boundaries of exotic $4$-manifolds
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by John B. Etnyre, Hyunki Min and Anubhav Mukherjee PDF
Trans. Amer. Math. Soc. 375 (2022), 4307-4332 Request permission

Abstract:

We give several criteria on a closed, oriented $3$-manifold that will imply that it is the boundary of a (simply connected) $4$-manifold that admits infinitely many distinct smooth structures. We also show that any weakly fillable contact $3$-manifold, or contact $3$-manifold with non-vanishing Heegaard Floer invariant, is the boundary of a simply connected $4$-manifold that admits infinitely many distinct smooth structures each of which supports a symplectic structure with concave boundary, that is there are infinitely many exotic caps for any such contact manifold.
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Additional Information
  • John B. Etnyre
  • Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia
  • MR Author ID: 619395
  • ORCID: 0000-0001-6061-0642
  • Email: etnyre@math.gatech.edu
  • Hyunki Min
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts
  • MR Author ID: 1403222
  • Email: hkmin@mit.edu
  • Anubhav Mukherjee
  • Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia
  • Email: anubhavmaths@gatech.edu
  • Received by editor(s): September 30, 2021
  • Received by editor(s) in revised form: October 28, 2021
  • Published electronically: January 20, 2022
  • Additional Notes: The authors were partially supported by NSF grant DMS-1608684 and DMS-1906414.
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 4307-4332
  • MSC (2020): Primary 57K41, 57K43
  • DOI: https://doi.org/10.1090/tran/8586
  • MathSciNet review: 4419060