1 Answers
Suspension is a construction passing from a map to a flow. Namely, let X {\displaystyle X} be a metric space, f : X → X {\displaystyle f:X\to X} be a continuous map and r : X → R + {\displaystyle r:X\to \mathbb {R} ^{+}} be a function bounded away from 0. Consider the quotient space:
The suspension of {\displaystyle } with roof function r {\displaystyle r} is the semiflow f t : X r → X r {\displaystyle f_{t}:X_{r}\to X_{r}} induced by the time translation T t : X × R → X × R , ↦ {\displaystyle T_{t}:X\times \mathbb {R} \to X\times \mathbb {R} ,\mapsto }.
If r ≡ 1 {\displaystyle r\equiv 1} , then the quotient space is also called the mapping torus of {\displaystyle }.