I have a question about the proof of the Arnold conjecture for monotone symplectic manifolds as it is explained in http://www.math.ethz.ch/~salamon/PREPRINTS/floer.pdf: Namely the author on page 32 says that the Arnold conjecture would immediately follow from a theorem 3.7 on the same page. But as far as I see, the theorem requires a further assumption on the Hamiltonian, namely that it has to be contained in some dense set $H_{\mbox{reg}}$ introduced on page 13. My question therefore is: How can we deduce the Arnold conjecture for a general Hamiltonian and not just for a generic one , from this construction of Floer homology? Or is the intention of the above paper to just prove the Arnold Conjecture for such a set of Hamiltonians and not necessarily for every Hamiltonian? Also I have found another point in the proof, which I am not sure about: Namely the author on page 23 has to introduce the Conley-Zehnder index and thus to assume that the $1$-periodic orbit is contractible to assign an index to him. I would then like to know: Does this really mean, we have to make a further restriction on the Hamiltonian and have to assume that every $1$-periodic orbit is contractible? Every help with one of these questions will be appreciated. It somehow looks to me as if ther
I have a question about the proof of the Arnold conjecture for monotone symplectic manifolds as it is explained in http://www.math.ethz.ch/~salamon/PREPRINTS/floer.pdf: Namely the author on page 32 says that the Arnold conjecture would immediately follow from a theorem 3.7 on the same page. But as far as I see, the theorem requires a further assumption on the Hamiltonian, namely that it has to be contained in some dense set $H_{\mbox{reg}}$ introduced on page 13. My question therefore is: How can we deduce the Arnold conjecture for a general Hamiltonian and not just for a generic one, from this construction of Floer homology?