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Variedades Diferenciables by Nogier, Yves

Variedades Diferenciables

by Yves Nogier , Jorge Sáenz
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Book cover type: Paperback
  • ISBN13: 9781545035962
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Createspace Independent Publishing Platform
  • Publisher Imprint: Createspace Independent Publishing Platform
  • Publication Date:
  • Pages: 234
  • Original Price: USD 19.99
  • Language: Spanish
  • Edition: 2
  • Item Weight: 381 grams
  • BISAC Subject(s): Geometry / Differential

En la presente edición la exposición de los conceptos y teoremas ha sido hecha con todo detalle buscando siempre la claridad, aún con perjuicio de la brevedad. Cada tema es ilustrado con numerosos ejemplos y problemas.El texto está dirigido a estudiantes de los últimos semestres de la Licenciatura en Matemáticas o Física, o a estudiantes que comienzan su postgrado, quienes deben estar familiarizados con la teoría de la diferenciación para funciones de varias variables y con los conceptos fundamentales de la Topología General. El texto ha sido sustancialmente aumentado, añadiendo nuevos capítulos que vienen a complementar el curso de Variedades con el curso de Formas Diferenciables dictado en el Decanato de Ciencias por uno de los autores. Estos últimos tres capítulos tratan de hacer de este texto, lo más completo posible para satisfacer las necesidades de la Licenciatura en Matemáticas, como la preparación de los lectores para los tiempos modernos, en los cuales, el uso y técnicas de las Variedades se ha hecho común tanto en las matemáticas puras como aplicadas.CONTENIDO: Capítulo 1. VARIEDADES DIFERENCIABLESHermann Weyl1.1. Variedades topológicas1.2. Ejemplos de variedades topológicas1.3. Estructuras Diferenciables1.4. Ejemplos de Variedades Diferenciables1.5. Funciones Diferenciables1.6. Partición de la unidad1.7. Los espacios proyectivos y las variedades de Grassmann1.7.1. Los Espacios Proyectivos Reales1.7.2. Variedades de GrassmannCapítulo 2. EL ESPACIO TANGENTE Y LA DERIVADASOPHUS LIE2.1. El espacio tangente 2.2. Derivada de una funciónCapítulo 3. SUBVARIEDADESHASSLER WHITNEY 3.1. Rango de una función 3.2. Inmersiones3.3. SubvariedadesCapítulo 4. EL FIBRADO TANGENTEÉLIE CARTAN4.1. Fibrados Vectoriales4.2. Variedades Definidas por una Familia de Inyecciones4.3. El Fibrado Tangente4.4. Campos Vectoriales4.5. Homomorfismo de Fibrado VectorialesCapítulo 5. FIBRADO COTANGENTE Y FIBRADOS TENSORIALESHENRI CARTAN5.1. Construcción de Fibrados5.2. El Fibrado Cotangente5.3. Producto Tensorial5.4. Campos TensorialesCapítulo 6. FORMAS DIFERENCIABLESALEXANDER GROTHENDIECK6.1. Preliminares algebraicos6.1.1. El producto cuña o producto exterior6.1.2. Orientación en espacios vectoriales6.2. k-formas diferenciables 6.3. La Derivada ExteriorCapítulo 7. INTEGRACIÓN DE FORMASGEORGES DE RHAM 7.1. Variedades orientables 7.2. Variedades con borde7.3. Integración de formas7.4. Teorema de StokesCapítulo 8. COHOMOLOGÍA DE LAS FORMAS DIFERENCIABLESJOHN MILNOR8.1. Cohomología de complejos de cadena8.1.1. Complejos de cadena8.1.2. Cohomología de un complejo de cadenas8.1.3. Homomorfismo de conexión y la secuencia larga de homología8.1.4. Homotopía de cadenas8.2. La cohomología de De Rham8.2.1. Operador de Homotopía y equivalencia homotópica8.2.2. Lema de Poincaré para la cohomología de De Rham8.2.3. La secuencia de Mayer-Vietoris para la cohomología de De Rham8.3. Cohomología de De Rham a soporte compacto8.4. Aplicaciones de la cohomología de De Rham8.4.1. El teorema de punto fijo de Brouwer8.4.2. El teorema de separación de Jordan8.4.3. El Teorema de invariancia de dominio de Brouwer

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