Artículo
Perfect discrete Morse functions on 2-complexes
Autor/es | Ayala Gómez, Rafael
Fernández Ternero, Desamparados Vilches Alarcón, José Antonio |
Departamento | Universidad de Sevilla. Departamento de Geometría y Topología |
Fecha de publicación | 2010 |
Fecha de depósito | 2015-06-29 |
Publicado en |
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Resumen | This paper is focused on the study of perfect discrete Morse functions on a 2-simplicial complex. These are those discrete Morse functions such that the number of critical i-simplices coincides with the i-th Betti number ... This paper is focused on the study of perfect discrete Morse functions on a 2-simplicial complex. These are those discrete Morse functions such that the number of critical i-simplices coincides with the i-th Betti number of the complex. In particular, we establish conditions under which a 2-complex admits a perfect discrete Morse function and conversely, we get topological properties of a 2-complex admitting such kind of functions. This approach is more general than the known results in the literature [7], since our study is not restricted to surfaces. These results can be considered as a first step in the study of perfect discrete Morse functions on 3-manifolds. |