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Large fluctuations in the electron column density can occur during thereionization process. We investigate the possibility of deriving the electrondensity fluctuations through detailed mapping of the redshifted 21-cm emissionfrom the neutral medium during reionization. We find that theelectron-scattering optical depth and 21-cm differential brightness temperatureare strongly anti-correlated, allowing optical depth estimates based entirelyon redshifted 21-cm measurements. This should help isolate the CMB polarizationfluctuations that are due to reionization, allowing both cleaning of the patchyreionization polarization signal as a contaminating source of confusion toother signals and a measurement of the primordial quadrupole that would bemeasured at various locations in the universe at the epoch of reionization.This latter application in principle allows mapping of the primordial densityfield at z~1100 over a large fraction of the Hubble volume.Comment: 4 pages, submitted to ApJ

Reconstructing the Thomson Optical Depth due to Patchy Reionization with 21 cm Fluctuation Maps