2022
DOI: 10.1142/s0129167x22500720
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On the Hofer–Zehnder conjecture on ℂPd via generating functions

Abstract: We use generating function techniques developed by Givental, Théret and ourselves to deduce a proof in [Formula: see text]Pd of the homological generalization of Franks theorem due to Shelukhin. This result proves in particular the Hofer–Zehnder conjecture in the nondegenerate case: every Hamiltonian diffeomorphism of [Formula: see text]Pd that has at least [Formula: see text] nondegenerate periodic points has infinitely many periodic points. Our proof does not appeal to Floer homology or the theory of [Formul… Show more

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(12 citation statements)
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“…By naturality of the properties stated in [All22a, Appendix A] and naturality of the homology projective joins, diagram (4) implies that these properties are still verified for our extension of the homology projective join to the weighted case: for instance, the homology projective join is associative, and it satisfies for every (disjoint) weighted projective spaces and .…”
Section: Preliminariesmentioning
confidence: 86%
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“…By naturality of the properties stated in [All22a, Appendix A] and naturality of the homology projective joins, diagram (4) implies that these properties are still verified for our extension of the homology projective join to the weighted case: for instance, the homology projective join is associative, and it satisfies for every (disjoint) weighted projective spaces and .…”
Section: Preliminariesmentioning
confidence: 86%
“…We can now extend the definition of to the weighted case by setting . Let us now get all the properties stated in [All22a, Appendix A] back in the weighted case.…”
Section: Preliminariesmentioning
confidence: 99%
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