Improper actions and simple connectivity at infinity
by
John Meier
Lafayette College

A locally finite CW complex X is simply connected at infinity if given any finite subcomplex C subset X, there is a finite subcomplex D subset X, such that loops outside of D are homotopically trivial outside of C. A finitely presented group G is simply connected at infinity if it acts freely and cocompactly on a 2-complex (e.g. the Cayley complex) which is simply connected at infinity.

In addition to being an interesting geometric property of G, connectivity at infinity is also related to questions about the dimension of G and whether or not G is a duality group. We will discuss how one can establish that G is simply connected at infinity if the action of G on X is not only not free, but is actually improper.

The argument uses the technology of complexes of groups, and can be generalized to higher dimensions using a spectral sequence argument provided by Ken Brown.

Date received: April 15, 1998