Aims. The aim of our new laboratory measurements is to measure accurate absolute oscillator strengths for neutral manganese transitions in the infrared needed for the study of late-type stars and ultracool dwarfs. Methods. Branching fractions have been measured by high resolution Fourier transform spectroscopy and combined with radiative level lifetimes in the literature to yield oscillator strengths. Results. We present experimental oscillator strengths for 20 Mn I transitions in the wavelength range 3216 to 13 997 angstrom, 15 of which are in the infrared. The transitions at 12 899 angstrom and 12 975 angstrom are observed as strong features in the spectra of late-type stars and ultracool dwarfs. We have fitted our calculated spectra to the observed Mn I lines in spectra of late-type stars. Using the new experimentally measured Mn I log(gf) values together with existing data for Mn I hyperfine structure splitting factors we determined the manganese abundance to be log N(Mn) = -6.65 +/- 0.05 in the atmosphere of the Sun, log N(Mn) = 6.95 +/- 0.20 in the atmosphere of Arcturus, and log N(Mn) = -6.70 +/- 0.20 in the atmosphere of M 9.5 dwarf 2MASSW 0140026+270150. (Less)