Representación finita de variedades
compactas

CARLOS MARIO PARRA^*, JOHANY SUÁREZ RAMÍREZ

Universidad Nacional de Colombia, Escuela de Matemáticas, Medellín, Colombia.

Resumen 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.

Palabras claves: Computabilidad y teoría de la recursión, topología algorítmica, variedades suaves.
MSC2010: 03D80, 57N13, 57N15, 57Q15, 57R55.

Finite representation of compact manifolds

Abstract 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

Keywords: Computability and recursion theory, algorithmic topology, smooth manifolds.

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^*E-mail: cmparra@unal.edu.co
Recibido: 26 de marzo de 2015, Aceptado: 18 de agosto de 2015.
Para citar este artículo: C.M Parra, J. Suárez Ramírez, Representación finita de variedades compactas, Rev. Integr. Temas Mat. 33 (2015), No. 2, 97-105.