## 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.## References

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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