Codimension One Foliation and the Prime Spectrum of a Ring

Authors

  • Badr Alharbi Umm Al-Qura University

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i1.4803

Keywords:

space of leaf classes., prime spectrum, Compact foliations

Abstract

Let F be a transversally oriented codimension-one foliation of class Cr, r ≥ 0, on a closed manifold M. A leaf class of a leaf F is the
union of all leaves having the same closure as F . Let X be the leaf classes space and X0 be the union of all open subsets of X homeomorphic to R or S1. In [2, Theorem 3.15] it is shown that if a codimension one foliation has a finite height, then the singular part of the space of leaf classes is homeomorphic to the prime spectrum (or simply the spectrum) of unitary commutative ring. In this paper we prove that the singular part of the space of leaf classes is homeomorphic to the spectrum of unitary commutative ring if and only if every family of totaly ordered leaves is bounded below.

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Published

2024-01-31

Issue

Section

Nonlinear Analysis

How to Cite

Codimension One Foliation and the Prime Spectrum of a Ring. (2024). European Journal of Pure and Applied Mathematics, 17(1), 356-361. https://doi.org/10.29020/nybg.ejpam.v17i1.4803