2016/03/10 by Mark Nieland, Nieland, Mark · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GN #math.GT #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1603.03269
arxiv created 2016/03/10 · openalex publication_date 2016/03/10 · arxiv updated 2016/03/11 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28
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.