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Palabras claves o descriptores: RATIONAL HOMOTOPY THEORY (Comienzo)
2 registros cumplieron la condición especificada en la base de información BIBCYT. ()
Registro 1 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Lupton, Gregory ; Christopher Philliips, N. ; L. Schochet, Claude
Título: Banach algebras and rational homotopy theory
Páginas/Colación: pp. 267-295
Fecha: January 2009
Transactions of the American Mathematical Society Vol. 361, no. 1 January 2009
Información de existenciaInformación de existencia

Palabras Claves: Palabras: COMMUTATIVE BANACH ALGEBRA COMMUTATIVE BANACH ALGEBRA, Palabras: FUNCTION SPACE FUNCTION SPACE, Palabras: GAUGE GROUPS GAUGE GROUPS, Palabras: GENERAL LINEAR GROUP GENERAL LINEAR GROUP, Palabras: MAXIMAL IDEAL SPACE MAXIMAL IDEAL SPACE, Palabras: RATIONAL H-SPACE RATIONAL H-SPACE, Palabras: RATIONAL HOMOTOPY THEORY RATIONAL HOMOTOPY THEORY, Palabras: SPACE OF LAST COLUMNS SPACE OF LAST COLUMNS

Resumen
It is proved herein that any absolute minimizer for a suitable Hamiltonian is a viscosity solution of the Aronsson equation:

Let $ A$be a unital commutative Banach algebra with maximal ideal space $ \operatorname{Max}(A).$We determine the rational H-type of $ \operatorname{GL}_n (A),$the group of invertible $ n \times n$matrices with coefficients in $ A,$in terms of the rational cohomology of $ \operatorname{Max} (A).$We also address an old problem of J. L. Taylor. Let $ \operatorname{Lc}_n (A)$denote the space of ``last columns'' of $ \operatorname{GL}_n (A).$We construct a natural isomorphism

$\displaystyle {\Check{H}}^s (\operatorname{Max} (A); \mathbb{Q} ) \cong \pi_{2 n - 1 - s} (\operatorname{Lc}_n (A)) \otimes \mathbb{Q} $

for $ n > \frac{1}{2} s + 1$which shows that the rational cohomology groups of $ \operatorname{Max} (A)$are determined by a topological invariant associated to $ A.$As part of our analysis, we determine the rational H-type of certain gauge groups $ F (X, G)$for $ G$a Lie group or, more generally, a rational H-space.

Registro 2 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Buijs, Urtzi ; Félix, Yves ; Murillo, Aniceto
Título: Lie models for the components of sections of a nilpotent fibration
Páginas/Colación: pp. 5601-5614
Fecha: October 2009
Transactions of the American Mathematical Society Vol. 361, no.10 October 2009
Información de existenciaInformación de existencia

Palabras Claves: Palabras: MAPPING SPACE MAPPING SPACE, Palabras: QUILLEN MODEL QUILLEN MODEL, Palabras: RATIONAL HOMOTOPY THEORY RATIONAL HOMOTOPY THEORY, Palabras: SPACE OF SECTIONS SPACE OF SECTIONS, Palabras: SULLIVAN MODEL SULLIVAN MODEL

Resumen
We give an explicit Lie model for any component of the space of free and pointed sections of a nilpotent fibration, and in particular, of the free and pointed mapping spaces. Among the applications presented, we obtain a Lie model of the exponential law and prove that, in many cases, the rank of the homotopy groups of the mapping space grows at the same rate as the rank of the homotopy groups of the target space.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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