Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The Seiberg-Witten equations and the length spectrum of hyperbolic three-manifolds
HTML articles powered by AMS MathViewer

by Francesco Lin and Michael Lipnowski HTML | PDF
J. Amer. Math. Soc. 35 (2022), 233-293 Request permission

Abstract:

We exhibit the first examples of hyperbolic three-manifolds for which the Seiberg-Witten equations do not admit any irreducible solution. Our approach relies on hyperbolic geometry in an essential way; it combines an explicit upper bound for the first eigenvalue on coexact $1$-forms $\lambda _1^*$ on rational homology spheres which admit irreducible solutions together with a version of the Selberg trace formula relating the spectrum of the Laplacian on coexact $1$-forms with the volume and complex length spectrum of a hyperbolic three-manifold. Using these relationships, we also provide precise numerical bounds on $\lambda _1^*$ for several hyperbolic rational homology spheres.
References
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC (2020): 57R58, 57K32
  • Retrieve articles in all journals with MSC (2020): 57R58, 57K32
Additional Information
  • Francesco Lin
  • Affiliation: Department of Mathematics, Columbia University, Room 509, MC 4406 2990 Broadway, New York, NY 10027
  • MR Author ID: 1169363
  • Email: flin@math.columbia.edu
  • Michael Lipnowski
  • Affiliation: Department of Mathematics and Statistics, McGill University, Burnside Hall, Room 1005, 805 Sherbrooke Street West, Montreal, Quebec, Canada H3A 0B9
  • MR Author ID: 1140735
  • Email: michael.lipnowski@mcgill.ca
  • Received by editor(s): November 21, 2018
  • Received by editor(s) in revised form: February 13, 2020, November 30, 2020, and March 22, 2021
  • Published electronically: August 2, 2021
  • Additional Notes: The first author was partially supported by NSF grant DMS-1807242
  • © Copyright 2021 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 35 (2022), 233-293
  • MSC (2020): Primary 57R58, 57K32
  • DOI: https://doi.org/10.1090/jams/982
  • MathSciNet review: 4322393