Connectivity at infinity for right angled Artin groups

We establish sufficient conditions implying semistability and connectivity at infinity properties for CAT(0) cubical complexes. We use this, along with the geometry of cubical K(π, 1)’s to give a complete description of the higher connectivity at infinity properties of right angled Artin groups. Among other things, this determines which right angled Artin groups are duality groups. Applications to group extensions are also included.

[1]  John Stallings,et al.  On Torsion-Free Groups with Infinitely Many Ends , 1968 .

[2]  R. Strebel.  A remark on subgroups of infinite index in Poincaré duality groups , 1977 .

[3]  Cohomology and the Behaviour at Infinity of Finitely Presented Groups , 1977 .

[4]  B. Jackson.  End invariants of group extensions , 1982 .

[5]  Kenneth S. Brown,et al.  Cohomology of Groups , 1982 .

[6]  Michael W. Davis.  Groups Generated by reflections and aspherical manifolds not covered by Euclidean space , 1983 .

[7]  M. Mihalik.  Semistability at the end of a group extension , 1983 .

[8]  R. Geoghegan,et al.  Free abelian cohomology of groups and ends of universal covers , 1985 .

[9]  Matthew G. Brin,et al.  3-manifolds which are end 1-movable , 1989 .

[10]  Using subnormality to show the simple connectivity at infinity of a finitely presented group , 1990 .

[11]  J. Meier,et al.  The Bieri–Neumann–Strebel Invariants for Graph Groups , 1993, math/9310202.

[12]  End invariants of the group of outer automorphisms of a free group , 1995 .

[13]  Semistability at infinity, simple connectivity at infinity and normal subgroups , 1996 .

[14]  M. Mihalik.  Semistability of Artin and Coxeter Groups , 1996 .

[15]  R. Geoghegan,et al.  The fundamental group at infinity , 1996 .

[16]  Geometric Invariants for Artin Groups , 1997 .

[17]  Noel Brady,et al.  Morse theory and finiteness properties of groups , 1997 .

[18]  Higher generation subgroup sets and the $ \Sigma $-invariants of graph groups , 1998 .

[19]  Michael W. Davis.  The cohomology of a Coxeter group with group ring coefficients , 1998 .

[20]  Mladen Bestvina.  Non-positively curved aspects of Artin groups of finite type , 1999 .

[21]  M. Bestvina,et al.  The topology at infinity of Out(Fn) , 2000 .

[22]  Improper actions and higher connectivity at infinity , 2000 .