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  "body": "\n## Summary\n\nThe suspension flow of an invertible map turns a discrete-time system into a continuous-time flow.\nEach point moves up at unit speed along a vertical segment whose height is given by a positive roof function.\nAt the top it jumps to the base above the image point.\nThe original map is recovered as the first-return map of the flow to the base.\nSuspensions with constant roof $1$ give the natural flow on the mapping torus.\nSuspensions with general roofs are a standard way to build examples of flows and to reduce flows to maps.\n\n## Explanations\n\n### L1 human\n\nPicture each point $x$ of a space sitting at the bottom of a vertical stick of height $r(x)$.\nA particle starts at the bottom of the stick, climbs at speed one, and when it reaches the top it is moved to the bottom of the stick over $T(x)$.\nWatching only the moments when particles are at the bottom shows the map $T$ step by step.\nFor example, with $T$ a rotation of a circle and $r = 1$, the space of all sticks is a torus, and the flow is a linear flow winding around it.\n",
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