The persistence of a relative Rabinowitz-Floer complex
| Autor: | Rizell, Georgios Dimitroglou, Sullivan, Michael G. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Geom. Topol. 28 (2024) 2145-2206 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/gt.2024.28.2145 |
| Popis: | We give a quantitative refinement of the invariance of the Legendrian contact homology algebra in general contact manifolds. We show that in this general case, the Lagrangian cobordism trace of a Legendrian isotopy defines a DGA stable tame isomorphism which is similar to a bifurcation invariance-proof for a contactization contact manifold. We use this result to construct a relative version of the Rabinowitz-Floer complex defined for Legendrians that also satisfies a quantitative invariance, and study its persistent homology barcodes. We apply these barcodes to prove several results, including: displacement energy bounds for Legendrian submanifolds in terms of the oscillatory norms of the contact Hamiltonians; a proof of Rosen and Zhang's non-degeneracy conjecture for the Shelukhin--Chekanov--Hofer metric on Legendrian submanifolds; and, the non-displaceability of the standard Legendrian real-projective space inside the contact real-projective space. Comment: Version 4 is substantially longer than prior versions because many details have been added (including new appendices A and B), as well as multiple explanatory figures. The conditions for Theorem 1.8 on interlinkedness have been corrected |
| Databáze: | arXiv |
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