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The post-merger product of the first binary neutron star merger eventdetected in gravitational waves, GW170817, depends on neutron star equation ofstate (EoS) and is not well determined. We generally discuss the constraintsone may pose on the maximum mass of a non-spinning neutron star, $M_{\rm TOV}$,based on the observations and some EoS-independent universal relations ofrapidly-spinning neutron stars. If the merger product is a black hole after abrief hypermassive neutron star (HMNS) phase, we derive $M_{\rm TOV} <2.09^{+0.11}_{-0.09}(^{+0.06}_{-0.04}) M_{\odot}$ at the 2$\sigma$ (1$\sigma$)level. The cases for a massive neutron star (MNS), either a supra-massiveneutron star (SMNS) or even a stable neutron star (SNS), are also allowed bythe data. We derive $2.09^{+0.11}_{-0.09}(^{+0.06}_{-0.04} M_{\odot}) \leqM_{\rm TOV}< 2.43^{+0.10}_{-0.08}(^{+0.06}_{-0.04}) M_{\odot}$ for the SMNScase and $M_{\rm TOV} \geq 2.43^{+0.10}_{-0.08}(^{+0.06}_{-0.04})M_{\odot}$ forthe SNS case, at the $2\sigma$ ($1\sigma$) confidence level. In the MNS cases,we also discuss the constraints on the neutron star parameters (the dipolarmagnetic field strength at the surface $B_p$ and the ellipticity $\epsilon$)that affect the spindown history, by considering different MNS survival times,e.g. 300 s, 1 d, and 155 d after the merger, as suggested by variousobservational arguments. We find that once an SMNS is formed, without violatingthe EM observational constraints, there always exist a set of ($B_p, \epsilon$)parameters that allow the SMNS to survive for 300s, 1 d, 155 d, or even longer.

What constraints on the neutron star maximum mass can one pose from GW170817 observations?