scholarly journals End invariants of the group of outer automorphisms of a free group

Topology ◽  
1995 ◽  
Vol 34 (3) ◽  
pp. 533-545 ◽  
Author(s):  
Karen Vogtmann
Keyword(s):  
Free Group ◽  
Outer Automorphisms

Out(F3) Index Realization

2015 ◽  
Vol 159 (3) ◽  
pp. 445-458 ◽  
Author(s):  
CATHERINE PFAFF
Keyword(s):  
Free Group ◽  
Quadratic Differentials ◽  
Singularity Index ◽  
Outer Automorphisms ◽  
Teichmüller Flow ◽  
Surface Homeomorphism

AbstractBy proving precisely which singularity index lists arise from the pair of invariant foliations for a pseudo-Anosov surface homeomorphism, Masur and Smillie [MS93] determined a Teichmüller flow invariant stratification of the space of quadratic differentials. In this paper we determine an analog to the theorem forOut(F3). That is, we determine which index lists permitted by the [GJLL98] index sum inequality are achieved by ageometric fully irreducible outer automorphisms of the rank-3 free group.

scholarly journals AN EQUIVARIANT WHITEHEAD ALGORITHM AND CONJUGACY FOR ROOTS OF DEHN TWIST AUTOMORPHISMS

2001 ◽  
Vol 44 (1) ◽  
pp. 117-141 ◽  
Author(s):  
Sava Krstić ◽  
Martin Lustig ◽  
Karen Vogtmann
Keyword(s):  
Free Group ◽  
Finite Groups ◽  
Linear Growth ◽  
Conjugacy Problem ◽  
Dehn Twist ◽  
Subject Classification ◽  
Finitely Generated ◽  
Finite Sets ◽  
Outer Automorphisms ◽  
Secondary 57M07

AbstractGiven finite sets of cyclic words $\{u_1,\dots,u_k\}$ and $\{v_1,\dots,v_k\}$ in a finitely generated free group $F$ and two finite groups $A$ and $B$ of outer automorphisms of $F$, we produce an algorithm to decide whether there is an automorphism which conjugates $A$ to $B$ and takes $u_i$ to $v_i$ for each $i$. If $A$ and $B$ are trivial, this is the classic algorithm due to Whitehead. We use this algorithm together with Cohen and Lustig’s solution to the conjugacy problem for Dehn twist automorphisms of $F$ to solve the conjugacy problem for outer automorphisms which have a power which is a Dehn twist. This settles the conjugacy problem for all automorphisms of $F$ which have linear growth.AMS 2000 Mathematics subject classification: Primary 20F32. Secondary 57M07

scholarly journals Local structure of some Out(Fn)-complexes

1990 ◽  
Vol 33 (3) ◽  
pp. 367-379 ◽  
Author(s):  
Karen Vogtmann
Keyword(s):  
Free Group ◽  
Finite Rank ◽  
Local Structure ◽  
Simplicial Complexes ◽  
Homotopy Equivalent ◽  
Outer Automorphisms ◽  
Finite Quotient

In previous work of the author and M. Culler, contractible simplicial complexes were constructed on which the group of outer automorphisms of a free group of finite rank acts with finite stabilizers and finite quotient. In this paper, it is shown that these complexes are Cohen-Macauley, a property they share with buildings. In particular, the link of a vertex in these complexes is homotopy equivalent to a wedge of spheres of codimension 1.

scholarly journals Irreducible outer automorphisms of a free group

1991 ◽  
Vol 111 (2) ◽  
pp. 309-309 ◽  
Author(s):  
S. M. Gersten ◽  
J. R. Stallings
Keyword(s):  
Free Group ◽  
Outer Automorphisms

scholarly journals Embedding the Picard group inside the class group: the case of $$\mathbb {Q}$$-factorial complete toric varieties

2021 ◽  
Author(s):  
Michele Rossi ◽  
Lea Terracini
Keyword(s):  
Free Group ◽  
Toric Variety ◽  
Class Group ◽  
Abelian Groups ◽  
Toric Varieties ◽  
Picard Group ◽  
Closed Field ◽  
Finitely Generated ◽  
Free Part ◽  
Canonical Injection

AbstractLet X be a $$\mathbb {Q}$$ Q -factorial complete toric variety over an algebraic closed field of characteristic 0. There is a canonical injection of the Picard group $$\mathrm{Pic}(X)$$ Pic ( X ) in the group $$\mathrm{Cl}(X)$$ Cl ( X ) of classes of Weil divisors. These two groups are finitely generated abelian groups; while the first one is a free group, the second one may have torsion. We investigate algebraic and geometrical conditions under which the image of $$\mathrm{Pic}(X)$$ Pic ( X ) in $$\mathrm{Cl}(X)$$ Cl ( X ) is contained in a free part of the latter group.

scholarly journals The minimally displaced set of an irreducible automorphism of $$F_N$$ is co-compact

2021 ◽  
Vol 116 (4) ◽  
pp. 369-383
Author(s):  
Stefano Francaviglia ◽  
Armando Martino ◽  
Dionysios Syrigos
Keyword(s):  
Growth Rate ◽  
Free Group ◽  
Exponential Growth ◽  
Single Point ◽  
Irreducible Automorphism

AbstractWe study the minimally displaced set of irreducible automorphisms of a free group. Our main result is the co-compactness of the minimally displaced set of an irreducible automorphism with exponential growth $$\phi $$ ϕ , under the action of the centraliser $$C(\phi )$$ C ( ϕ ) . As a corollary, we get that the same holds for the action of $$ <\phi>$$ < ϕ > on $$Min(\phi )$$ M i n ( ϕ ) . Finally, we prove that the minimally displaced set of an irreducible automorphism of growth rate one consists of a single point.

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