Single crossovers in circular pieces of DNA do not seem to be a big topic, because if they happened, they would lead to a kind of combined chromosome with two inner strands and one large outer strand. (A bit like an 8)
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But do these single crossovers actually not occur, for example because the crossover machinery is physically not able to do it, or do we just not observe them because they will inevitably lead to cell death and/or the chromosome somehow breaking?