DNA within chromosomes in the nucleus is non-randomly organized into chromosome territories, compartments and topologically associated domains (TADs). Chromosomal rearrangements have the potential to alter chromatin organization and modify gene expression leading to selection against these structural variants. Drosophila pseudoobscura has a wealth of naturally occurring gene arrangements that were generated by overlapping inversion mutations caused by two chromosomal breaks that rejoin the central region in reverse order. Unlike humans, Drosophila inversion heterozygotes do not have negative effects associated with crossing over during meiosis because males use achiasmate mechanisms for proper segregation, and aberrant recombinant meiotic products generated in females are lost in polar bodies. As a result, Drosophila populations are found to harbour extensive inversion polymorphisms. It is not clear, however, whether chromatin architecture constrains which inversions breakpoints persist in populations. We mapped the breakpoints of seven inversions in D. pseudoobscura to the TAD map to determine if persisting inversion breakpoints are more likely to occur at boundaries between TADs. Our results show that breakpoints occur at TAD boundaries more than expected by chance. Some breakpoints may alter gene expression within TADs supporting the hypothesis that position effects contribute to inversion establishment. This article is part of the theme issue ‘Genomic architecture of supergenes: causes and evolutionary consequences’.