2011/12/01 by Tomoo Matsumura, Matsumura, Tomoo, W. Frank Moore +1 · 1 citation
Mathematics · #14M25 #16S37 #53D99 #55N91 #57R18 #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Symplectic Geometry (math.SG) #math.AC #math.AT #math.SG #msc:14M25 #msc:16S37 #msc:53D99 #msc:55N91 #msc:57R18
paper · pdf · doi:10.48550/arxiv.1112.0157
14 pages
openalex publication_date 2011/12/01 · arxiv created 2012/06/11 · arxiv updated 2012/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we discuss the connected sum K1#Z K2 of simplicial complexes K1 and K2, 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. We show that the Stanley-Reisner ring of a connected sum K1#Z K2 is the connected sum of the Stanley-Reisner rings of K1 and K2 along the Stanley-Reisner ring of the intersection of K1 and K2. The strong connected sum K1 #Z K2 is defined in such a way that when K1 and K2 are Gorenstein, and Z is a suitable subset of the intersection of K1 and K2, then the Stanley-Reisner ring of the connected sum is Gorenstein, by the work of Ananthnarayan-Avramov-Moore. These algebraic computations can be interpreted in terms of the equivariant cohomology of moment angle complexes and we also describe the symplectic cut of a toric orbifold in terms of moment angle complexes.