# MAA

## Seminar

### Homotopy types of fibres of pfaffian maps

Seminar Room 1, Newton Institute

#### Abstract

We prove a tight upper bound on the number of different homotopy types of fibres of semialgebraic, quadratic or semi-Pfaffian maps in terms of formats of these maps. A similar argument leads to a tight upper bound on the sizes of finite bisimulations of Pfaffian dynamical and hybrid systems.