  The 2nd generation VLTI instrument GRAVITY is a two-field infrared
interferometer operating in the K band between 1.97 and 2.43 $\mu$m with either
the four 8 m or the four 1.8 m telescopes of the Very Large Telescope (VLT).
Beams collected by the telescopes are corrected with adaptive optics systems
and the fringes are stabilized with a fringe-tracking system. A metrology
system allows the measurement of internal path lengths in order to achieve
high-accuracy astrometry. High sensitivity and high interferometric accuracy
are achieved thanks to (i) correction of the turbulent phase, (ii) the use of
low-noise detectors, and (iii) the optimization of photometric and coherence
throughput. Beam combination and most of the beam transport are performed with
single-mode waveguides in vacuum and at low temperature. In this paper, we
present the functions and performance achieved with weakly birefringent
standard single-mode fiber systems in GRAVITY. Fibered differential delay lines
(FDDLs) are used to dynamically compensate for up to 6 mm of delay between the
science and reference targets. Fibered polarization rotators allow us to align
polarizations in the instrument and make the single-mode beam combiner close to
polarization neutral. The single-mode fiber system exhibits very low
birefringence (less than 23{\deg}), very low attenuation (3.6-7 dB/km across
the K band), and optimized differential dispersion (less than 2.04 $\mu$rad cm2
at zero extension of the FDDLs). As a consequence, the typical fringe contrast
losses due to the single-mode fibers are 6% to 10% in the lowest-resolution
mode and 5% in the medium- and high-resolution modes of the instrument for a
photometric throughput of the fiber chain of the order of 90%. There is no
equivalent of this fiber system to route and modally filter beams with delay
and polarization control in any other K-band beamcombiner.
