Connected-sum decompositions of surfaces with minimally-intersecting filling pairs
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Let Sg be a closed surface of genus g and let (α, β) be a filling pair on Sg; then i(α, β) ≥ 2g−1, where i is the (geometric) intersection number. Aougab and Huang demonstrated that (exponentially many) minimally-intersecting filling pairs exist on Sg when g > 2 by a construction which produces higher-genus surfaces with filling pairs as connected sums of lower-genus surfaces with filling pairs. We present a generalization of their construction which provides an explicit, algebraic means of determining the homeomorphism class of the resulting pair, and a criterion for determining when a surface with minimally-intersecting filling pair admits a decomposition as a connected sum.