The Arnold conjecture for singular symplectic manifolds

In this article, we study the Hamiltonian dynamics on singular symplectic manifolds and prove the Arnold conjecture for a large class of bm-symplectic manifolds. More precisely, we prove a lower bound on the number 1-periodic Hamiltonian orbits for b2m-symplectic manifolds depending only on the topology of the manifold. Moreover, for bm-symplectic surfaces, we improve the lower bound depending on the topology of the pair (M, Z). We then venture into the study of Floer homology to this singular realm and we conclude with a list of open questions.
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