On transversality with deficiency and a conjecture of sard

Carlos Biasi, Osamu Saeki

研究成果: ジャーナルへの寄稿記事

2 引用 (Scopus)

抄録

Let f : M → N be a Cr map between Cr manifolds (r ≥ 1) and K a Cr manifold. In this paper, by using the Sard theorem, we study the topological properties of the space of Cr maps g : K → N which satisfy a certain transversality condition with respect to f in a weak sense. As an application, by considering the case where K is a point, we obtain some new results about the topological properties of f(Rq(f)), where Rq(f) is the set of points of M where the rank of the differential of f is less than or equal to q. In particular, we show a result about the topological dimension of f(Rq(f)), which is closely related to a conjecture of Sard concerning the Hausdorff measure of f(Rq(f)).

元の言語英語
ページ(範囲)5111-5122
ページ数12
ジャーナルTransactions of the American Mathematical Society
350
発行部数12
出版物ステータス出版済み - 1998
外部発表Yes

Fingerprint

CR Manifold
Transversality
Topological Properties
Transversality Condition
Hausdorff Measure
Less than or equal to
Set of points
Theorem

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

これを引用

On transversality with deficiency and a conjecture of sard. / Biasi, Carlos; Saeki, Osamu.

:: Transactions of the American Mathematical Society, 巻 350, 番号 12, 1998, p. 5111-5122.

研究成果: ジャーナルへの寄稿記事

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