Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T06:26:16.085Z Has data issue: false hasContentIssue false
  • English
  • Français

MORSE INEQUALITIES ON CERTAIN INFINITE 2-COMPLEXES

Published online by Cambridge University Press:  09 August 2007

R. AYALA ,
L. M. FERNÁNDEZ  and
J. A. VILCHES
R. AYALA
Affiliation:
Dpto. de Geometría y Topología, Universidad de Sevilla, 41080, Sevilla, Spain e-mails: rdayala@us.es, lmfer@us.es, vilches@us.es
L. M. FERNÁNDEZ
Affiliation:
Dpto. de Geometría y Topología, Universidad de Sevilla, 41080, Sevilla, Spain e-mails: rdayala@us.es, lmfer@us.es, vilches@us.es
J. A. VILCHES
Affiliation:
Dpto. de Geometría y Topología, Universidad de Sevilla, 41080, Sevilla, Spain e-mails: rdayala@us.es, lmfer@us.es, vilches@us.es
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Using the notion of discrete Morse function introduced by R. Forman for finite cw-complexes, we generalize it to the infinite 2-dimensional case in order to get the corresponding version of the well-known discrete Morse inequalities on a non-compact triangulated 2-manifold without boundary and with finite homology. We also extend them for the more general case of a non-compact triangulated 2-pseudo-manifold with a finite number of critical simplices and finite homology.

Keywords

57M2057Q1568R10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 2 , May 2007 , pp. 155 - 165
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

REFERENCES

1. Ayala, R., Fernández, L. M. and Vilches, J. A., Desigualdades de Morse generalizadas sobre grafos, Actas de las III jornadas de matemática discreta y algorítmica (Universidad de Sevilla, Sevilla, 2002), 159–164.Google Scholar
2. Diestel, R., Graph theory, Graduate texts in mathematics, No. 173 (Springer-Verlag, 1997).Google Scholar
3. Forman, R., Combinatorial differential topology and geometry, New perspectives in geometric combinatorics (MSRI Publications, No. 38, 1999), 177–206.Google Scholar
4. Forman, R., Morse theory for cell complexes, Adv. Math. 134 (1998), 90–145.CrossRefGoogle Scholar
5. Forman, R., Combinatorial vector fields and dynamical systems, Math. Z. 228 (1998), 629–681.CrossRefGoogle Scholar
6. Lewiner, T., Lopes, H. and Tavares, G., Optimal discrete Morse functions for 2-manifolds, in Computational geometry: theory and applications (Elsevier Science, 2003), 221–233.Google Scholar
7. Munkres, J. R., Elements of algebraic topology (Addison-Wesley, 1984).Google Scholar
8. Vilches, J. A., Funciones de Morse dicretas sobre complejos infinitos, Ph.D. Thesis (Universidad de Sevilla, Sevilla, 2003).Google Scholar