Using simplicial volume to count multi-tangent trajectories of traversing vector fields
For a non-vanishing gradient-like vector field on a compact manifold X[superscript n+1] with boundary, a discrete set of trajectories may be tangent to the boundary with reduced multiplicity n, which is the maximum possible. (Among them are trajectories that are tangent to ∂X exactly n times.) We pr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer Netherlands,
2016-12-15T23:21:08Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | For a non-vanishing gradient-like vector field on a compact manifold X[superscript n+1] with boundary, a discrete set of trajectories may be tangent to the boundary with reduced multiplicity n, which is the maximum possible. (Among them are trajectories that are tangent to ∂X exactly n times.) We prove a lower bound on the number of such trajectories in terms of the simplicial volume of X by adapting methods of Gromov, in particular his "amenable reduction lemma". We apply these bounds to vector fields on hyperbolic manifolds. |
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