A -dimensional generic flow is a pair with a smooth compact oriented -manifold and a smooth nowhere-zero vector field on having generic behavior along ; on the set of such pairs we consider the equivalence relation generated by topological equivalence (homeomorphism mapping oriented orbits to oriented orbits) and by homotopy with fixed configuration on the boundary, and we denote by the quotient set. In this paper we provide a combinatorial presentation of . To do so we introduce a certain class of finite -dimensional polyhedra with extra combinatorial structures, and some moves on , exhibiting a surjection such that if and only if and are related by the moves. To obtain this result we first consider the subset of consisting of flows having all orbits homeomorphic to closed segments or points, constructing a combinatorial counterpart for , and then adapting it to .
"Generic flows on -manifolds." Kyoto J. Math. 55 (1) 143 - 167, April 2015. https://doi.org/10.1215/21562261-2848142