Bouquets of circles for lamination languages and complexities
LaBRI – UFR Math-Info, University of Bordeaux 1,
Accepted: 17 March 2014
Laminations are classic sets of disjoint and non-self-crossing curves on surfaces. Lamination languages are languages of two-way infinite words which code laminations by using associated labeled embedded graphs, and which are subshifts. Here, we characterize the possible exact affine factor complexities of these languages through bouquets of circles, i.e. graphs made of one vertex, as representative coding graphs. We also show how to build families of laminations together with corresponding lamination languages covering all the possible exact affine complexities.
Mathematics Subject Classification: 14Q05 / 37B10 / 37F20 / 57R30 / 68R15 / 68Q45 / 68R10
Key words: Curves / laminations on surfaces / symbolic dynamics / shifts / factor complexity / embedded graphs / train-tracks / Rauzy graphs / substitutions / spirals
© EDP Sciences 2014