1,521 research outputs found
Finiteness of outer automorphism groups of random right-angled Artin groups
We consider the outer automorphism group Out(A_Gamma) of the right-angled
Artin group A_Gamma of a random graph Gamma on n vertices in the Erdos--Renyi
model. We show that the functions (log(n)+log(log(n)))/n and
1-(log(n)+log(log(n)))/n bound the range of edge probability functions for
which Out(A_Gamma) is finite: if the probability of an edge in Gamma is
strictly between these functions as n grows, then asymptotically Out(A_Gamma)
is almost surely finite, and if the edge probability is strictly outside of
both of these functions, then asymptotically Out(A_Gamma) is almost surely
infinite. This sharpens results of Ruth Charney and Michael Farber from their
preprint "Random groups arising as graph products", arXiv:1006.3378v1.Comment: 29 pages. Mostly rewritten, results tightened, statements corrected,
gaps fille
On the second homology group of the Torelli subgroup of Aut(F_n)
Let IA_n be the Torelli subgroup of Aut(F_n). We give an explicit finite set
of generators for H_2(IA_n) as a GL_n(Z)-module. Corollaries include a version
of surjective representation stability for H_2(IA_n), the vanishing of the
GL_n(Z)-coinvariants of H_2(IA_n), and the vanishing of the second rational
homology group of the level l congruence subgroup of Aut(F_n). Our generating
set is derived from a new group presentation for IA_n which is infinite but
which has a simple recursive form.Comment: 39 pages; minor revision; to appear in Geom. Topo
A Birman exact sequence for the Torelli subgroup of Aut(F_n)
We develop an analogue of the Birman exact sequence for the Torelli subgroup
of Aut(F_n). This builds on earlier work of the authors who studied an analogue
of the Birman exact sequence for the entire group Aut(F_n). These results play
an important role in the authors' recent work on the second homology group of
the Torelli group.Comment: 31 pages, minor revision; to appear in Int. J. Algebr. Compu
Symplectic structures on right-angled Artin groups: between the mapping class group and the symplectic group
We define a family of groups that include the mapping class group of a genus
g surface with one boundary component and the integral symplectic group
Sp(2g,Z). We then prove that these groups are finitely generated. These groups,
which we call mapping class groups over graphs, are indexed over labeled
simplicial graphs with 2g vertices. The mapping class group over the graph
Gamma is defined to be a subgroup of the automorphism group of the right-angled
Artin group A_Gamma of Gamma. We also prove that the kernel of the map Aut
A_Gamma to Aut H_1(A_Gamma) is finitely generated, generalizing a theorem of
Magnus.Comment: 45 page
The Relationship of Supervisors\u27 Attachment Styles to their Perceptions of Self-Efficacy in Providing Corrective Feedback and to the Working Alliance in Counselor Education
Supervisors are largely responsible for the structuring of supervision in counseling, which is influenced by various factors pertaining to a supervisor, all of which greatly affect the development of the counselor trainee. This study was designed to explore the factors of attachment styles, self-efficacy for giving corrective feedback and the dimensions of the working alliance. The results will ultimately inform counselor educators and supervisors about the practice of supervision and the implications of supervisors’ attachment styles in counselor supervision
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