MICC swMATH ID: 16450 Software Authors: Glenn, Paul; Menasco, William W.; Morrell, Kayla; Morse, Matthew J. Description: MICC: A tool for computing short distances in the curve complex. The complex of curves π(S g ) of a closed orientable surface of genus gβ₯2 is the simplicial complex whose vertices, π 0 (S g ), are isotopy classes of essential simple closed curves in S g . Two vertices co-bound an edge of the 1-skeleton, π 1 (S g ), if there are disjoint representatives in S g . A metric is obtained on π 0 (S g ) by assigning unit length to each edge of π 1 (S g ). Thus, the distance between two vertices, d(v,w), corresponds to the length of a geodesic β a shortest edge-path between v and w in π 1 (S g ). In Birman et al. (2016), the authors introduced the concept of efficient geodesics in π 1 (S g ) and used them to give a new algorithm for computing the distance between vertices. In this note, we introduce the software package MICC (Metric in the Curve Complex), a partial implementation of the efficient geodesic algorithm. We discuss the mathematics underlying MICC and give applications. In particular, up to an action of an element of the mapping class group, we give a calculation which produces all distance 4 vertex pairs for g=2 that intersect 12 times, the minimal number of intersections needed for this distance and genus. Homepage: https://micc.github.io/ Keywords: mapping class group; curve complex; distance; geodesic Related Software: Curver; CPLEX Cited in: 5 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year MICC: a tool for computing short distances in the curve complex. Zbl 1347.57020Glenn, Paul; Menasco, William W.; Morrell, Kayla; Morse, Matthew J. 2017 all top 5 Cited by 11 Authors 3 Menasco, William W. 2 Birman, Joan S. 2 Morse, Matthew J. 1 Chang, Hong 1 Glenn, Paul G. 1 Jin, XiFeng 1 Mahanta, Kuwari 1 Margalit, Dan 1 Morrell, Kayla 1 Palaparthi, Sreekrishna 1 Wrinkle, Nancy C. Cited in 4 Serials 2 Topology and its Applications 1 Geometriae Dedicata 1 Mathematische Annalen 1 Journal of Symbolic Computation Cited in 5 Fields 4 Manifolds and cell complexes (57-XX) 3 Group theory and generalizations (20-XX) 2 Differential geometry (53-XX) 1 Combinatorics (05-XX) 1 Several complex variables and analytic spaces (32-XX) Citations by Year