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Geometrically, the connected sum is motivated by Lerman's symplectic cut applied to a toric orbifold, and algebraically, it is motivated by the connected sum of rings introduced by Ananthnarayan-Avramov-Moore.\n  We show that the Stanley-Reisner ring of a connected sum K_1#^Z K_2 is the connected sum of the Stanley-Reisner rings of K_1 and K_2 along the Stanley-Reisner ring of the intersection of K_1 and K_2. 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Frank Moore","submitted_at":"2011-12-01T12:28:44Z","abstract_excerpt":"In this paper, we discuss the connected sum K_1#^Z K_2 of simplicial complexes K_1 and K_2, as well as define the notion of a strong connected sum. Geometrically, the connected sum is motivated by Lerman's symplectic cut applied to a toric orbifold, and algebraically, it is motivated by the connected sum of rings introduced by Ananthnarayan-Avramov-Moore.\n  We show that the Stanley-Reisner ring of a connected sum K_1#^Z K_2 is the connected sum of the Stanley-Reisner rings of K_1 and K_2 along the Stanley-Reisner ring of the intersection of K_1 and K_2. 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