Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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.

 

Riemannian nilmanifolds and the trace formula
HTML articles powered by AMS MathViewer

by Ruth Gornet PDF
Trans. Amer. Math. Soc. 357 (2005), 4445-4479 Request permission

Abstract:

This paper examines the clean intersection hypothesis required for the expression of the wave invariants, computed from the asymptotic expansion of the classical wave trace by Duistermaat and Guillemin. The main result of this paper is the calculation of a necessary and sufficient condition for an arbitrary Riemannian two-step nilmanifold to satisfy the clean intersection hypothesis. This condition is stated in terms of metric Lie algebra data. We use the calculation to show that generic two-step nilmanifolds satisfy the clean intersection hypothesis. In contrast, we also show that the family of two-step nilmanifolds that fail the clean intersection hypothesis are dense in the family of two-step nilmanifolds. Finally, we give examples of nilmanifolds that fail the clean intersection hypothesis.
References
Similar Articles
Additional Information
  • Ruth Gornet
  • Affiliation: Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76019-0408
  • Email: rgornet@uta.edu
  • Received by editor(s): August 28, 2003
  • Published electronically: June 10, 2005
  • Additional Notes: This material is based in part on work supported by the Texas Advanced Research Program under Grant No. 003644-002 and by NSF grants DMS-9753220 (preliminary) and DMS-0204648
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 4445-4479
  • MSC (2000): Primary 35P20, 58J53, 53C22; Secondary 58J40, 22E25
  • DOI: https://doi.org/10.1090/S0002-9947-05-03965-6
  • MathSciNet review: 2156717