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COMD Learning Seminar Series: Spaces Of Branched Coverings
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For every $n,d$, the space of degree-$d$ bicritical branched coverings of $S^2$ with a critical cycle of length $n$ is connected. This is a topological analogue of questions raised in the talks by Tanya Firsova and Eko Hironaka. I will prove this result, explaining along the way why it is essentially a group-theoretical question.
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