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 cobound an edge of the 1skeleton, 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 edgepath 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 1347.57020 Glenn, Paul; Menasco, William W.; Morrell, Kayla; Morse, Matthew J. 
2017

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top 5
Cited by 11 Authors
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 (57XX) 
3  Group theory and generalizations (20XX) 
2  Differential geometry (53XX) 
1  Combinatorics (05XX) 
1  Several complex variables and analytic spaces (32XX) 