  Neutralino annihilations in the Sun to weak boson and top quark pairs lead to
high-energy neutrinos that can be detected by the IceCube and KM3 experiments
in the search for neutralino dark matter. We calculate the neutrino signals
from real and virtual WW, ZZ, Zh, and $t \bar t$ production and decays,
accounting for the spin-dependences of the matrix elements, which can have
important influences on the neutrino energy spectra. We take into account
neutrino propagation including neutrino oscillations, matter-resonance,
absorption, and nu_tau regeneration effects in the Sun and evaluate the
neutrino flux at the Earth. We concentrate on the compelling Focus Point (FP)
region of the supergravity model that reproduces the observed dark matter relic
density. For the FP region, the lightest neutralino has a large bino-higgsino
mixture that leads to a high neutrino flux and the spin-dependent neutralino
capture rate in the Sun is enhanced by 10^3 over the spin-independent rate. For
the standard estimate of neutralino captures, the muon signal rates in IceCube
are identifiable over the atmospheric neutrino background for neutralino masses
above M_Z up to 400 GeV.
