Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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.


These are the differentials of order $n$
HTML articles powered by AMS MathViewer

by Dan Laksov and Anders Thorup PDF
Trans. Amer. Math. Soc. 351 (1999), 1293-1353 Request permission


We answer P.-A. Meyer’s question “Qu’est ce qu’une différentielle d’ordre $n$?”. In fact, we present a general theory of higher order differentials based upon a construction of universal objects for higher order differentials. Applied to successive tangent spaces on a differentiable manifold, our theory gives the higher order differentials of Meyer as well as several new results on differentials on differentiable manifolds. In addition our approach gives a natural explanation of the quite mysterious multiplicative structure on higher order differentials observed by Meyer. Applied to iterations of the first order Kähler differentials our theory gives an algebra of higher order differentials for any smooth scheme. We also observe that much of the recent work on higher order osculation spaces of varieties fits well into the framework of our theory.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 13N05, 14F10, 16Sxx
  • Retrieve articles in all journals with MSC (1991): 13N05, 14F10, 16Sxx
Additional Information
  • Dan Laksov
  • Affiliation: KTH, S–100 44 Stockholm, Sweden
  • Email:
  • Anders Thorup
  • Affiliation: Matematisk Afdeling, Københavns Universitet, Universitetsparken 5, DK–2100 København Ø, Denmark
  • Email:
  • Received by editor(s): January 30, 1997
  • Additional Notes: The first author was partially supported by The Göran Gustafsson Foundation for Research in Natural Sciences and Medicine.
    The second author was supported in part by the Danish Natural Science Research Council, grant 11–7428.
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 1293-1353
  • MSC (1991): Primary 13N05, 14F10; Secondary 16Sxx
  • DOI:
  • MathSciNet review: 1458328