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- W2529040010 abstract "We prove three theorems based on lemmas of Gromovinvolving the simplicial norm on stratified spaces. First, theGromov singular fiber theorem (with proof originally sketched byGromov) relates the simplicial norm to the number of maximummultiplicity critical points of a smooth map of manifolds thatdrops in dimension by 1. Second, the multitangent trajectorytheorem (proved with Gabriel Katz) relates the simplicial norm tothe number of maximum-multiplicity tangent trajectories of anowhere-vanishing gradient-like vector field on a manifold withboundary. And third, the Morse broken trajectory theorem relatesthe simplicial volume to the number of maximally brokentrajectories of the gradient flow of a Morse – Smale function.Corollary: a Morse function on a closed hyperbolic manifold musthave a critical point of every Morse index." @default.
- W2529040010 created "2016-10-14" @default.
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- W2529040010 date "2016-01-01" @default.
- W2529040010 modified "2023-10-16" @default.
- W2529040010 title "Special gradient trajectories counted by simplex straightening" @default.
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