TY - JOUR

T1 - On definite lattices bounded by integer surgeries along knots with slice genus at most 2

AU - Golla, Marco

AU - Scaduto, Christopher

N1 - Funding Information:
Received by the editors October 1, 2018, and, in revised form, February 11, 2019 and February 12, 2019. 2010 Mathematics Subject Classification. Primary 57M25, 57M27. 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.
Funding Information:
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. We would like to thank Carlos Rito for his assistance with computations with rational cuspidal curves (which were unsuccessful and did not make it to the paper). We also thank the organizers of the July 2018 conference Gauge Theory and Applications at the University of Regensburg for their hospitality and support. Finally, we thank the referee for their useful comments and suggestions.
Publisher Copyright:
© 2019 American Mathematical Society

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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.

AB - 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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U2 - 10.1090/tran/7823

DO - 10.1090/tran/7823

M3 - Article

AN - SCOPUS:85075132077

VL - 372

SP - 7805

EP - 7829

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 11

ER -