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Topological types of Pfaffian manifolds

Published online by Cambridge University Press:  22 January 2016

Masato Fujita  and
Masahiro Shiota
Masato Fujita
Affiliation:
Department of Mathematics, Graduate School of Science, Kyoto University, Sakyou Kyoto, 606-8502, Japan, fujita@kusm.kyoto-u.ac.jp
Masahiro Shiota
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa Nagoya, 464-8601, Japan, shiota@math.nagoya-u.ac.jp
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Abstract

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Let Ω = (ω1,…,ωn-k) be differential 1-forms with polynomial coefficients in Rn. A Pfaffian manifold of Ω is by definition a maximal integral k-manifold of Ω. It is shown that the number of homeomorphism classes of all Pfaffian manifolds of Rolle Type of Ω is finite and, moreover, bounded by a computable function in variables n, k and the degree of ω1,…, ωn-k. Finiteness is proved also in any o-minimal structure.

We give also an example of a semi-algebraic C1 differential form on a semi-algebraic C2 3-manifold whose Pfaffian manifolds have homeomorphism classes of the cardinality of continuum. Hence the cardinality of all manifolds is the continuum (not countable).

Keywords

03C6414P1058A17
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 173 , 2004 , pp. 1 - 22
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

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