Navegar

Colección

Datos Estadísticas

Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In this paper we extend the classical theory of combinatorial manifolds to the non-homogeneous setting. NH-manifolds are polyhedra which are locally like Euclidean spaces of varying dimensions. We show that many of the properties of classical manifolds remain valid in this wider context. NH-manifolds appear naturally when studying Pachner moves on (classical) manifolds. We introduce the notion of NH-factorization and prove that PL-homeomorphic manifolds are related by a finite sequence of NH-factorizations involving NH-manifolds. © 2012 The Managing Editors.

Registro:

Documento: Artículo
Título:Non-homogeneous combinatorial manifolds
Autor:Capitelli, N.A.; Minian, E.G.
Filiación:Departamento de Matemática-IMAS, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:Collapses; Combinatorial manifolds; Pachner moves; Shellability; Simplicial complexes
Año:2013
Volumen:54
Número:1
Página de inicio:419
Página de fin:439
DOI: http://dx.doi.org/10.1007/s13366-012-0114-6
Título revista:Beitrage zur Algebra und Geometrie
Título revista abreviado:Beitr. Algebr. Geom.
ISSN:01384821
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01384821_v54_n1_p419_Capitelli

Referencias:

  • Alexander, J.W., The combinatorial theory of complexes (1930) Ann. Math., 31, pp. 294-322
  • Björner, A., Las Vergnas, M., Sturmfels, B., White, N., Ziegler, G., (1999) Oriented Matroids, , 2nd edn. Cambridge University Press, London
  • Björner, A., Wachs, M., Shellable nonpure complexes and posets. I (1996) Trans. Am. Math. Soc., 348 (4), pp. 1299-1327
  • Glaser, L., (1970) Geometrical Combinatorial Topology, I. , van Nostrand Reinhold Company, New York
  • Hudson, J.F.P., (1969) Piecewise Linear Topology, , W. A. Benjamin
  • Kozlov, D., Combinatorial algebraic topology (2008) Algorithms and Computation in Mathematics, 21. , Springer, Berlin
  • Lickorish, W.B.R., Simplicial moves on complexes and manifolds (1999) Geom. Topol. Monogr., 2, pp. 299-320
  • Lickorish, W.B.R., Unshellable triangulations of spheres (1991) Eur. J. Combin., 12, pp. 527-530
  • Munkres, J.R., (1984) Elements of Algebraic Topology, , Addison-Wesley Publishing Co., Menlo Park
  • Newman, M.H.A., On the foundation of combinatorial analysis situs (1926) Proc. R. Acad. Amst., 29, pp. 610-641
  • Pachner, U., PL homeomorphic manifolds are equivalent by elementary shellings (1991) Eur. J. Combin., 12, pp. 129-145
  • Rourke, C.P., Sanderson, B.J., (1972) Introduction to Piecewise-Linear Topology, , Springer, Berlin
  • Spanier, E., (1966) Algebraic Topology, , Springer, Berlin
  • Whitehead, J.H.C., Simplicial spaces, nuclei and m-groups (1939) Proc. Lond. Math. Soc., 45, pp. 243-327
  • Ziegler, G.M., Shelling polyhedral 3-balls and 4-polytopes (1998) Discret. Comput. Geom., 19, pp. 159-174

Citas:

---------- APA ----------
Capitelli, N.A. & Minian, E.G. (2013) . Non-homogeneous combinatorial manifolds. Beitrage zur Algebra und Geometrie, 54(1), 419-439.
http://dx.doi.org/10.1007/s13366-012-0114-6
---------- CHICAGO ----------
Capitelli, N.A., Minian, E.G. "Non-homogeneous combinatorial manifolds" . Beitrage zur Algebra und Geometrie 54, no. 1 (2013) : 419-439.
http://dx.doi.org/10.1007/s13366-012-0114-6
---------- MLA ----------
Capitelli, N.A., Minian, E.G. "Non-homogeneous combinatorial manifolds" . Beitrage zur Algebra und Geometrie, vol. 54, no. 1, 2013, pp. 419-439.
http://dx.doi.org/10.1007/s13366-012-0114-6
---------- VANCOUVER ----------
Capitelli, N.A., Minian, E.G. Non-homogeneous combinatorial manifolds. Beitr. Algebr. Geom. 2013;54(1):419-439.
http://dx.doi.org/10.1007/s13366-012-0114-6