The mapping class group of a minimal subshift

The Mapping Class Group of a Genus

Mapping class group of a handlebody

Let B be a 3-dimensional handlebody of genus g. Let M be the group of the isotopy classes of orientation preserving homeomorphisms of B. We construct a 2-dimensional simplicial complex X, connected and simply-connected, on which M acts by simplicial transformations and has only a finite number of orbits. From this action we derive an explicit finite presentation ofM. We consider a 3-dimensional...

Complex Chaotic Behavior of a Class of Subshift Cellular Automata

A class of parameterized boolean, one-dimensional, biinfinite cellular autom at a has been st udied and t heir behavior observed when some param eters of the local funct ion are changed. T hese aut omata are equivalent to a par t icular class of boolean neural networks and t he change in t he parameters corresponds to a change in the symmetricity of t he connect ion matrix. T he purpo se is to ...

On a substitution subshift related to the Grigorchuk group

The substitution acts on words (finite sequences) over this alphabet as well as on infinite sequences. It is easy to observe that τ has a unique invariant sequence ω that is the limit of words τ (a), k = 1, 2, . . . . Let Ω be the smallest closed set of one-sided infinite sequences over the alphabet {a, b, c, d} that contains ω and is invariant under the shift σ (σ acts on sequences by deleting...

Actions of the Mapping Class Group

Let S be a closed oriented surface S of genus g ≥ 0 with m ≥ 0 marked points (punctures) and 3g − 3 + m ≥ 2. This is a survey of recent results on actions of the mapping class group of S which led to a geometric understanding of this group. Mathematics Subject Classification (2010). Primary 30F60, Secondary 20F28, 20F65, 20F69