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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 definite lattices bounded by integer surgeries along knots with slice genus at most 2
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by Marco Golla and Christopher Scaduto PDF
Trans. Amer. Math. Soc. 372 (2019), 7805-7829 Request permission


We classify the positive definite intersection forms that arise from smooth 4-manifolds with torsion-free homology bounded by positive integer surgeries on the right-handed trefoil. A similar, slightly less complete classification is given for the $(2,5)$-torus knot, and analogous results are obtained for integer surgeries on knots of slice genus at most 2. The proofs use input from Yang–Mills instanton gauge theory, Heegaard Floer correction terms, and the topology of singular complex plane curves.
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Additional Information
  • Marco Golla
  • Affiliation: CNRS, Laboratoire de Mathématiques Jean Leray, 44322 Nantes, France
  • MR Author ID: 1098550
  • Email:
  • Christopher Scaduto
  • Affiliation: Simons Center for Geometry and Physics, SUNY Stony Brook University, Stony Brook, New York 11794
  • MR Author ID: 1122383
  • Email:
  • Received by editor(s): October 1, 2018
  • Received by editor(s) in revised form: February 11, 2019, and February 12, 2019
  • Published electronically: June 21, 2019
  • Additional Notes: The first author acknowledges support from CNRS though a “Jeunes chercheurs et jeunes chercheuses” grant and hospitality from the Simons Center for Geometry and Physics.
    The second author was supported by NSF grant DMS-1503100.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 7805-7829
  • MSC (2010): Primary 57M25, 57M27
  • DOI:
  • MathSciNet review: 4029682