Remote Access Transactions of the American Mathematical Society
Green Open Access

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.
MSC (2010): Primary 57M25, 57M27
DOI: https://doi.org/10.1090/tran/7823
Published electronically: June 21, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 57M25, 57M27

Retrieve articles in all journals with MSC (2010): 57M25, 57M27


Additional Information

Marco Golla
Affiliation: CNRS, Laboratoire de Mathématiques Jean Leray, 44322 Nantes, France
Email: marco.golla@univ-nantes.fr

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

DOI: https://doi.org/10.1090/tran/7823
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