  We present a theoretical study on photonic topological crystals whose
symmetry is governed by quantum valley-Hall topological insulators and whose
propagating edge modes are strongly confined due to bowtie geometries.
Dielectric bowtie structures exploit the field discontinuities at boundaries
between materials with different refractive indices, and here bowties emerge at
the topological interface due to the close proximity of two triangular features
in the underlying crystal. The topological bowtie mode features a unit-cell
mode volume down to $8\times10^{-4}$ cubic wavelengths at the center of the
bowtie bridge of width $10~\text{nm}$, and we show that it is possible to use
perturbed versions of the unit cells as building blocks for topological
heterostructure bowtie cavities with quality factors exceeding $10^7$. Due to
the tightly confined bowtie mode, this implies a strongly enhanced light-matter
interaction as quantified by a Purcell factor of $3 \times 10^6$.
