### Abstract

Let f : M → N and g : K → N be generic differentiable maps of compact manifolds without boundary into a manifold such that their intersection satisfies a certain transversality condition. We show, under a certain cohomological condition, that if the images f(M) and g(K) intersect, then the (ν + 1)th Betti number of their union is strictly greater than the sum of their (ν + 1)th Betti numbers, where ν = dim M + dim K - dim N. This result is applied to the study of coincidence sets and fixed point sets.

Original language | English |
---|---|

Pages (from-to) | 31-46 |

Number of pages | 16 |

Journal | Topology and its Applications |

Volume | 95 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1999 |

### All Science Journal Classification (ASJC) codes

- Geometry and Topology

## Fingerprint Dive into the research topics of 'On the Betti number of the union of two generic map images'. Together they form a unique fingerprint.

## Cite this

Biasi, C., Libardi, A. K. M., & Saeki, O. (1999). On the Betti number of the union of two generic map images.

*Topology and its Applications*,*95*(1), 31-46. https://doi.org/10.1016/s0166-8641(97)00273-3