Representación finita de variedades compactas

• Parra, Carlos Mario ^[1] ; Suárez Ramírez, Johany ^[1]
  1. [1] Universidad Nacional de Colombia

     Universidad Nacional de Colombia

     Colombia

     
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 33, Nº. 2, 2015 (Ejemplar dedicado a: REVISTA INTEGRACIÓN), págs. 97-105
• Idioma: español
• DOI: 10.18273/revint.v33n2-2015001
• Títulos paralelos:
  • Finite representation of compact manifolds
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Un logro notable de la topología algorítmica es el resultado de A.A. Márkov sobre la insolubilidad del problema del homeomorfismo para variedades. Posteriormente, Boone, Haken y Poénaru extendieron la idea original de Márkov al caso de variedades suaves cerradas. Una primera dificultad era la introducción de una representación finita de una variedad diferenciable o combinatórica que la describiese de forma natural. En este trabajo extendemos dicha representación a variedades suaves compactas y proponemos una definición de variedad suave representable.

  • English

    A remarkable achievement of algorithmic topology is A.A.Markov’s theorem on the unsolvability of the homeomorphism problem for manifolds. Boone, Haken and Poénaru extended Markov’s original proof to the case of closed smooth manifolds. One of their initial difficulties was the introduction of a natural finite representation of a differentiable and/or combinatorial manifold. In this paper we extend this representation to compact smooth manifolds and propose an extension to smooth manifolds.

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