Biblioteca de la Universidad Complutense de Madrid

Inverse sequences, rooted trees and their end spaces

Impacto

Martínez Pérez , Álvaro y Morón, Manuel A. (2010) Inverse sequences, rooted trees and their end spaces. Topology and its Applications, 157 (16). pp. 2480-2494. ISSN 0166-8641

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 31 Diciembre 2020.

290kB

URL Oficial: http://www.sciencedirect.com/science/article/pii/S0166864110002634




Resumen

In this paper we prove that if we consider the standard real metric on simplicial rooted trees then the category Tower-Set of inverse sequences can be described by means of the bounded coarse geometry of the naturally associated trees. Using this we give a geometrical characterization of Mittag-Leffler property in inverse sequences in terms of the metrically proper homotopy type of the corresponding tree and its maximal geodesically complete subtree. We also obtain some consequences in shape theory. In particular we describe some new representations of shape morphisms related to infinite branches in trees.


Tipo de documento:Artículo
Palabras clave:Tree; Inverse sequence; End space; Coarse map; Mittag-Leffler property; Shape theory
Materias:Ciencias > Matemáticas > Topología
Ciencias > Matemáticas > Álgebra
Código ID:14996
Referencias:

[1] H.J. Baues, A. Quintero, Infinite Homotopy Theory, Kluwer Academic Publishers, Boston, 2001.

[2] M. Bestvina, R-trees in topology, geometry and group theory, in: Handbook of Geometric Topology, North-Holland, Amsterdam, 2002, pp. 55–91.

[3] K. Borsuk, Theory of Retracts, Polish Scientific Publishers, Warszawa, 1967.

[4] K. Borsuk, Theory of Shape, Monogr. Mat., vol. 59, Polish Scientific Publishers, Warszawa, 1975.

[5] J.-M. Cordier, T. Porter, Shape Theory. Categorical Methods of Approximation, Math. Appl., Ellis Horwood Ltd., Halsted Press, John Wiley and Sons, Inc., Chichester, New York, 1989.

[6] J. Dydak, J. Segal, Shape Theory. An Introduction, Lecture Notes in Math., vol. 688, Springer-Verlag, Berlin, Heidelberg, New York, 1978.

[7] A. Grothendieck, Technique de descente et théorèmes d’existence en géométrie algébrique II, in: Séminaire Bourbaki, 12 ème année, 1959–1960, exposé pp. 190–195.

[8] B. Hughes, Trees and ultrametric spaces: a categorial equivalence, Adv. Math. 189 (2004) 148–191.

[9] B. Hughes, Trees, ultrametrics, and noncommutative geometry, arXiv:math/0605131v2[math.OA].

[10] S. Mac Lane, Categories for the Working Mathematician, Springer-Verlag, New York, 1971.

[11] S. Mardešic, J. Segal, Shapes of compacta and ANR systems, Fund. Math. 72 (1971) 41–59.

[12] S. Mardešic, J. Segal, Shape Theory, North-Holland, 1982.

[13] Á. Martínez-Pérez, M.A. Morón, Uniformly continuous maps between ends of R-trees, Math. Z. 263 (3) (2009) 583–606.

[14] J.W. Morgan, _-trees and their applications, Bull. Amer. Math. Soc. 26 (1) (1992) 87–112.

[15] M.A. Morón, F.R. Ruiz del Portal, Shape as a Cantor completion process, Math. Z. 225 (1997) 67–86.

[16] A.M. Robert, A Course in p-Adic Analysis, Grad. Texts in Math., vol. 198, Springer, 2000.

[17] J. Roe, Lectures on Coarse Geometry, Univ. Lecture Ser., vol. 31, Amer. Math. Soc., 2003.

[18] J. Roe, Coarse cohomology and index theory on complete Riemannian manifolds, Mem. Amer. Math. Soc. 497 (1993).

[19] J.P. Serre, Trees, Springer-Verlag, New York, 1980.

Depositado:25 Abr 2012 08:47
Última Modificación:06 Feb 2014 10:13

Sólo personal del repositorio: página de control del artículo