It is a well-known result that a closed manifold that admits a nonsingular flow (ie a flow without fixed points) only if its Euler Characteristic is zero. We provide a short proof of this by constructing a cell complex on the ambient manifold that is induced by the flow and showing that this complex has zero Euler Characteristic. We use the method of a global transverse disk with the hope that this method will be useful in studying global topological properties of nonsingular flows.
Department, Program, or Center
School of Mathematical Sciences (COS)
Basener, William, "A short constructive proof that nonsingular flows only exist on manifolds of zero Euler characteristic" (2007). Accessed from
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