Integral Arnol'd Conjecture
| Autor: | Rezchikov, Semon |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We explain how to adapt the methods of Abouzaid-McLean-Smith to the setting of Hamiltonian Floer theory. We develop a language around equivariant ``$\langle k \rangle$-manifolds'', which are a type of manifold-with-corners that suffices to capture the combinatorics of Floer-theoretic constructions. We describe some geometry which allows us to straightforwardly adapt Lashofs's stable equivariant smoothing theory and Bau-Xu's theory of FOP-perturbations to $\langle k \rangle$-manifolds. This allows us to compatibly smooth global Kuranishi charts on all Hamiltonian Floer trajectories at once, in order to extract a Floer complex and prove the Arnol'd conjecture over the integers. We also make first steps towards a further development of the theory, outlining the analog of bifurcation analysis in this setting, which can give short independence proofs of the independence of Floer-theoretic invariants of all choices involved in their construction. Comment: 56 pages |
| Databáze: | arXiv |
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