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Computing o-minimal topological invariants using differential topology
Author(s):
Ya'acov
Peterzil;
Sergei
Starchenko
Journal:
Trans. Amer. Math. Soc.
359
(2007),
1375-1401.
MSC (2000):
Primary 03C64, 03C98, 57R99
Posted:
October 24, 2006
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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
Email:
kobi@math.haifa.ac.il
Sergei
Starchenko
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email:
starchenko.1@nd.edu
DOI:
10.1090/S0002-9947-06-04220-6
PII:
S 0002-9947(06)04220-6
Keywords:
O-minimality
Received by editor(s):
June 20, 2005
Posted:
October 24, 2006
Additional Notes:
The second author was supported in part by NSF Grant \#0400163
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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