In the mathematical subject geometric group theory, a fully irreducible automorphism of the free group Fn is an element of Out(Fn) which has no periodic conjugacy classes of proper free factors in Fn (where n > 1). Fully irreducible automorphisms are also referred to as "irreducible with irreducible powers" or "iwip" automorphisms. The notion of being fully irreducible provides a key Out(Fn) counterpart of the notion of a pseudo-Anosov element of the mapping class group of a finite type surface. Fully irreducibles play an important role in the study of structural properties of individual elements and of subgroups of Out(Fn).
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In the mathematical subject geometric group theory, a fullyirreducibleautomorphism of the free group Fn is an element of Out(Fn) which has no periodic...
complicated. In their 1992 paper Bestvina and Handel proved that every irreducibleautomorphism of Fn has a train-track representative. In the same paper they...
group associated to G2 is the automorphism group of the octonions, and the group associated to F4 is the automorphism group of a certain Albert algebra...
described in the next section. There is a unique minimal way of cutting an irreducible oriented 3-manifold along tori into pieces that are Seifert manifolds...
this realization of spinors as (complex) column vectors will either be irreducible if the dimension is odd, or it will decompose into a pair of so-called...
topological space. Since the connected components refine the irreducible components any irreducible scheme is connected but not vice versa. An affine scheme...
S2CID 119779011. Roychowdhury, Mrinal Kanti; Rudolph, Daniel J. (2009). "Any two irreducible Markov chains are finitarily orbit equivalent". Israel Journal of Mathematics...
Gruppen und ihr Analogon bei nicht kommutativen Gruppen" [The Theory of Automorphism-Rings of Abelian Groups and Their Analogs in Noncommutative Groups]....
{\mathcal {F}}_{n}^{(1)}} if and only if φ {\displaystyle \varphi } is fullyirreducible. There exists a coarsely Lipschitz coarsely Out ( F n ) {\displaystyle...
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