Suspension (dynamical systems)

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

Suspension is a construction passing from a map to a flow. Namely, let be a metric space, be a continuous map and be a function (roof function or ceiling function) bounded away from 0. Consider the quotient space

The suspension of with roof function is the semiflow[1] induced by the time translation .

If , then the quotient space is also called the mapping torus of .


  1. ^ M. Brin and G. Stuck, Introduction to Dynamical Systems, Cambridge University Press, 2002.