Atlas: Simple Connectivity at Infinity and Artin Groups by John Meier

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G^3 = Geometric Groups on the Gulf coast
May 28-29, 1999
University of South Alabama
Mobile, AL, USA

Organizers
Phil Bowers, Stephen Brick, Jon Corson

Simple Connectivity at Infinity and Artin Groups
by
John Meier
Lafayette College
Coauthors: Ken Brown (Cornell University)

A locally finite CW-complex is 1-connected at infinity if, roughly speaking, circles near infinity can be filled by disks near infinity. This property has proven to be important in the study of 3-manifolds as well as duality properties of infinite groups.

Let G be a finitely presented group, acting on a simply connected complex X with G finite. A nice geometric argument shows that if the stabilizer of each cell "C" is (1-|C|)-connected at infinity, then G is itself 1-connected at infinity.

Regretably this argument doesn't immediately apply to the action of an Artin group on the Charney-Davis modified Deligne complex. However, by tweaking the argument, one can gain insight into which Artin groups are simply connected at infinity.

Date received: May 11, 1999