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Computing o-minimal topological invariants using differential topology

Authors: Ya'acov Peterzil and Sergei Starchenko
Journal: Trans. Amer. Math. Soc. 359 (2007), 1375-1401
MSC (2000): Primary 03C64, 03C98, 57R99
Published electronically: October 24, 2006
MathSciNet review: 2262855
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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

Sergei Starchenko
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

Keywords: O-minimality
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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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