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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.

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Computing o-minimal topological invariants using differential topology
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by Ya’acov Peterzil and Sergei Starchenko PDF
Trans. Amer. Math. Soc. 359 (2007), 1375-1401 Request permission

Abstract:

We work in an o-minimal expansion of a real closed field. Using piecewise smoothness of definable functions we define the topological degree for definable continuous functions. Using this notion of the degree we obtain a new proof for the existence of torsion points in a definably compact group, and also a new proof of an o-minimal analogue of the Brouwer fixed point theorem.
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Additional Information
  • Ya’acov Peterzil
  • Affiliation: Department of Mathematics, University of Haifa, Haifa, Israel
  • Email: kobi@math.haifa.ac.il
  • Sergei Starchenko
  • Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
  • MR Author ID: 237161
  • Email: starchenko.1@nd.edu
  • Received by editor(s): June 20, 2005
  • Published electronically: October 24, 2006
  • Additional Notes: The second author was supported in part by NSF Grant #0400163
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 1375-1401
  • MSC (2000): Primary 03C64, 03C98, 57R99
  • DOI: https://doi.org/10.1090/S0002-9947-06-04220-6
  • MathSciNet review: 2262855