  Topology is central to understanding and engineering materials that display
robust physical phenomena immune to imperfections. The topological character of
a material is quantified by topological invariants that simplify the
classification of topological phases. In energy-conserving systems, the
topological invariants, e.g., the Chern number, are determined by the winding
of the eigenstates in momentum (wavevector) space, which have been
experimentally measured in ultracold atoms, microwaves, and photonic systems.
Recently, new topological phenomena have been theoretically uncovered in
dissipative, non-Hermitian systems. A novel, non-Hermitian topological
invariant, yet to be observed in experiments, is predicted to emerge from the
winding of the complex eigenvalues in momentum space. Here, we directly measure
the non-Hermitian topological invariant arising from spectral degeneracies
(exceptional points) in the momentum space of exciton polaritons. These hybrid
light-matter quasiparticles are formed by photons strongly coupled to
electron-hole pairs (excitons) in a halide perovskite semiconductor microcavity
at room temperature. By performing momentum-resolved photoluminescence
spectroscopy of exciton polaritons, we map out both the real (energy) and
imaginary (linewidth) parts of the exciton-polariton eigenvalues near the
exceptional point, and extract a new topological invariant - fractional
spectral winding. Our work represents an essential step towards realisation of
non-Hermitian topological phases in a solid-state system.
