English

Reeb spaces of smooth functions on manifolds II

Geometric Topology 2023-08-14 v1

Abstract

The Reeb space of a continuous function is the space of connected components of the level sets. In this paper we characterize those smooth functions on closed manifolds whose Reeb spaces have the structure of a finite graph. We also give several explicit examples of smooth functions on closed manifolds such that they themselves or their Reeb spaces have some interesting properties.

Keywords

Cite

@article{arxiv.2308.05953,
  title  = {Reeb spaces of smooth functions on manifolds II},
  author = {Osamu Saeki},
  journal= {arXiv preprint arXiv:2308.05953},
  year   = {2023}
}

Comments

11 pages, 6 figures, continuation of the previous paper "Reeb spaces of smooth functions on manifolds"