Using simplicial volume to count multi-tangent trajectories of traversing vector fields
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10711_2015_Article_104.pdf
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Author(s)
Alpert, Hannah
Katz, Gabriel
Date Issued
August 2015
Journal
Geometriae Dedicata
Publisher
Springer Netherlands
Citation
Alpert, Hannah, and Gabriel Katz. “Using Simplicial Volume to Count Multi-Tangent Trajectories of Traversing Vector Fields.” Geom Dedicata 180, no. 1 (August 4, 2015): 323–338.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10711-015-0104-6
