  We analyze the topology and dispersion of bulk Wannier excitons in nanosheets
of topological insulators in the family of bismuth chalcogenides. Our main
finding is that excitons inherit the topology of the electronic bands,
quantified by the skyrmion winding numbers of the constituent electron and hole
pseudospins as a function of the total exciton momentum. Every $s$-wave exciton
state consists of a quartet with a degenerate and quadratically dispersing
non-chiral doublet, and a chiral doublet with one linearly dispersing mode as
in transition metal dichalcogenides.
