| Full text | |
| Author(s): |
Batista, Erica Boizan
;
Ferreira Costa, Joao Carlos
;
Nuno-Ballesteros, Juan J.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | JOURNAL OF SINGULARITIES; v. 22, p. 10-pg., 2020-01-01. |
| Abstract | |
Let N be a smooth compact, connected and orientable 2-manifold with or without boundary. Given a stable circle-valued function gamma : N -> S-1, we introduced a topological invariant associated to gamma, called generalized Reeb graph. It is a generalized version of the classical and well known Reeb graph. The purpose of this paper is to investigate the number of loops in generalized Reeb graphs associated to stable circle-valued functions gamma : N -> S-1. We show that the number of loops depends on the genus of N, the number of boundary components of N, and the number of open saddles of gamma. In particular, we show a class of functions whose generalized Reeb graphs have the maximal number of loops. (AU) | |
| FAPESP's process: | 18/25157-3 - Invariants of real singularities, pairs of germs and classification problems |
| Grantee: | João Carlos Ferreira Costa |
| Support Opportunities: | Regular Research Grants |