Feuilletages et topologie spectrale

Ezzeddine Bouacida; Othman Echi; Ezzeddine Salhi

doi:10.2969/jmsj/05220447

Feuilletages et topologie spectrale

Ezzeddine Bouacida
, Othman Echi
, Ezzeddine Salhi

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

Let ℱ be a codimension-one foliation, transversally oriented, of class C^r(r≥0) on a connected closed manifold M. The class of a leaf F of ℱ is defined to be the union of all leaves G with F¯=G¯. Let X be the space of classes of leaves in M and let X0 be the union of open subsets of X which are homeomorphic to R or to S¹. In this paper we prove that if the level of ℱ is well defined (in the sense of [12]), then X-X₀ is a spectral space.

Original language	English
Pages (from-to)	447-464
Number of pages	18
Journal	Journal of the Mathematical Society of Japan
Volume	52
Issue number	2
DOIs	https://doi.org/10.2969/jmsj/05220447
State	Published - 2000
Externally published	Yes

Keywords

Foliation
Leaf
Spectrum of a ring
Zariski topology

ASJC Scopus subject areas

General Mathematics

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10.2969/jmsj/05220447

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title = "Feuilletages et topologie spectrale",

abstract = "Let ℱ be a codimension-one foliation, transversally oriented, of class Cr(r≥0) on a connected closed manifold M. The class of a leaf F of ℱ is defined to be the union of all leaves G with F¯=G¯. Let X be the space of classes of leaves in M and let X0 be the union of open subsets of X which are homeomorphic to R or to S1. In this paper we prove that if the level of ℱ is well defined (in the sense of [12]), then X-X0 is a spectral space.",

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author = "Ezzeddine Bouacida and Othman Echi and Ezzeddine Salhi",

year = "2000",

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language = "English",

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AU - Bouacida, Ezzeddine

AU - Echi, Othman

AU - Salhi, Ezzeddine

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N2 - Let ℱ be a codimension-one foliation, transversally oriented, of class Cr(r≥0) on a connected closed manifold M. The class of a leaf F of ℱ is defined to be the union of all leaves G with F¯=G¯. Let X be the space of classes of leaves in M and let X0 be the union of open subsets of X which are homeomorphic to R or to S1. In this paper we prove that if the level of ℱ is well defined (in the sense of [12]), then X-X0 is a spectral space.

AB - Let ℱ be a codimension-one foliation, transversally oriented, of class Cr(r≥0) on a connected closed manifold M. The class of a leaf F of ℱ is defined to be the union of all leaves G with F¯=G¯. Let X be the space of classes of leaves in M and let X0 be the union of open subsets of X which are homeomorphic to R or to S1. In this paper we prove that if the level of ℱ is well defined (in the sense of [12]), then X-X0 is a spectral space.

KW - Foliation

KW - Leaf

KW - Spectrum of a ring

KW - Zariski topology

UR - https://www.scopus.com/pages/publications/0040808945

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DO - 10.2969/jmsj/05220447

M3 - Article

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EP - 464

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

IS - 2

ER -

Feuilletages et topologie spectrale

Abstract

Keywords

ASJC Scopus subject areas

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