Abstract
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We show that if
is a space of holonomic solutions with space of formal solutions
that satisfies a certain
relative
-principle, then
the nonrelative map
admits a section up to homotopy. We apply this to the relative
-principle
for overtwisted contact structures proved by Borman, Eliashberg and Murphy to
find infinite cyclic subgroups in the homotopy groups of contactomorphism
groups.
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Keywords
contact geometry, $h$-principle
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Mathematical Subject Classification
Primary: 53D35, 57R17
Secondary: 58D99
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Publication
Received: 29 March 2023
Revised: 18 December 2023
Accepted: 31 January 2024
Published: 5 March 2025
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| © 2025 MSP (Mathematical Sciences
Publishers). Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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