We first derive a simple Euler characteristic formula for simplicial maps, based on their fibers. As applications, we give several formulas relating the Euler characteristics and the numbers of singularities of smooth generic maps in explicit situations, among which are singular surfaces in 3-dimensional manifolds, Morse functions on surfaces, stable maps of 4-dimensional manifolds into 3-dimensional manifolds, etc.
|Number of pages||17|
|Journal||Journal of Geometry|
|Publication status||Published - Oct 2008|
All Science Journal Classification (ASJC) codes
- Geometry and Topology