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Transactions of the American Mathematical Society

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

 
 

 

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


Authors: Marco Golla and Christopher Scaduto
Journal: Trans. Amer. Math. Soc. 372 (2019), 7805-7829
MSC (2010): Primary 57M25, 57M27
DOI: https://doi.org/10.1090/tran/7823
Published electronically: June 21, 2019
MathSciNet review: 4029682
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Abstract: 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: marco.golla@univ-nantes.fr

Christopher Scaduto
Affiliation: Simons Center for Geometry and Physics, SUNY Stony Brook University, Stony Brook, New York 11794
MR Author ID: 1122383
Email: cscaduto@scgp.stonybrook.edu

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.
Article copyright: © Copyright 2019 American Mathematical Society