Inicio Nosotros Búsquedas
Buscar en nuestra Base de Datos:     
Título: =Transverse LS Category For Rienmannian Foliations
Sólo un registro cumplió la condición especificada en la base de información BIBCYT.
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Hurder, Steven ; Töben, Dirk
Título: Transverse LS Category For Rienmannian Foliations
Páginas/Colación: pp. 5647-5680
Fecha: November 2009
Transactions of the American Mathematical Society Vol. 361, no.11 November 2009
Información de existenciaInformación de existencia

Palabras Claves: Palabras: COMPACT HAUSDORFF FOLIATION COMPACT HAUSDORFF FOLIATION, Palabras: EPSTEIN FILTRATION EPSTEIN FILTRATION, Palabras: LUSTERNIK-SCHNIRELMANN CATEGORY LUSTERNIK-SCHNIRELMANN CATEGORY, Palabras: RIEMANNIAN FOLIATION RIEMANNIAN FOLIATION, Palabras: RIEMANNIAN SUBMERSION RIEMANNIAN SUBMERSION

Resumen
We study the transverse Lusternik-Schnirelmann category theory of a Riemannian foliation on a closed manifold

We study the transverse Lusternik-Schnirelmann category theory of a Riemannian foliation $ \mathcal{F}$on a closed manifold $ M$. The essential transverse category $ \operatorname{cat}^e_{\mathbin{\cap{\mkern-9mu}\mid} }(M,\mathcal{F})$is introduced in this paper, and we prove that $ \operatorname{cat}^e_{\mathbin{\cap{\mkern-9mu}\mid} }(M,\mathcal{F})$is always finite for a Riemannian foliation. Necessary and sufficient conditions are derived for when the usual transverse category $ \operatorname{cat}_{\mathbin{\cap{\mkern-9mu}\mid} }(M,\mathcal{F})$is finite, and thus $ \operatorname{cat}^e_{\mathbin{\cap{\mkern-9mu}\mid} }(M,\mathcal{F}) = \operatorname{cat}_{\mathbin{\cap{\mkern-9mu}\mid} }(M,\mathcal{F})$holds.

A fundamental point of this paper is to use properties of Riemannian submersions and the Molino Structure Theory for Riemannian foliations to transform the calculation of $ \operatorname{cat}^e_{\mathbin{\cap{\mkern-9mu}\mid} }(M,\mathcal{F})$into a standard problem about $ \mathbf O(q)$-equivariant LS category theory. A main result, Theorem 1.6, states that for an associated $ \mathbf O(q)$-manifold $ \widehat W$, we have that $ \operatorname{cat}^e_{\mathbin{\cap{\mkern-9mu}\mid} }(M,\mathcal{F}) = \operatorname{cat}_{\mathbf O(q)}(\widehat W)$. Hence, the traditional techniques developed for the study of smooth compact Lie group actions can be effectively employed for the study of the LS category of Riemannian foliations.

A generalization of the Lusternik-Schnirelmann theorem is derived: given a $ C^1$-function $ f \colon M \to \mathbb{R}$which is constant along the leaves of a Riemannian foliation $ \mathcal{F}$, the essential transverse category $ \operatorname{cat}^e_{\mathbin{\cap{\mkern-9mu}\mid} }(M,\mathcal{F})$is a lower bound for the number of critical leaf closures of $ f$.

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno

Generados por el servidor 'bibcyt.ucla.edu.ve' (3.146.255.127)
Adaptive Server Anywhere (07.00.0000)
ODBC
Sesión="" Sesión anterior=""
 ejecutando Back-end Alejandría BE 7.0.7b0 ** * *
3.146.255.127 (NTM) bajo el ambiente Apache/2.2.4 (Win32) PHP/5.2.2.
usando una conexión ODBC (RowCount) al manejador de bases de datos..
Versión de la base de información BIBCYT: 7.0.0 (con listas invertidas [2.0])

Cliente: 3.146.255.127
Salida con Javascript
** Back-end Alejandría BE 7.0.7b0 *