Memoirs of the American Mathematical Society 1992; 86 pp; softcover Volume: 98 ISBN10: 0821825313 ISBN13: 9780821825310 List Price: US$29 Individual Members: US$17.40 Institutional Members: US$23.20 Order Code: MEMO/98/471
 In the study of the proper homotopy theory of finitely presented groups, semistability at infinity is an end invariant of central importance. A finitely presented group that is semistable at infinity has a welldefined fundamental group at infinity independent of base ray. If \(G\) is semistable at infinity, then \(G\) has free abelian second cohomology with \({\mathbb Z}G\) coefficients. In this work, the authors show that amalgamated products and HNNextensions of finitely presented semistable at infinity groups are also semistable at infinity. A major step toward determining whether all finitely presented groups are semistable at infinity, this result easily generalizes to finite graphs of groups. In an early application, this result was used in showing that all onerelator groups are semistable at infinity. The theory of group actions on trees and techniques derived from the proof of Dunwoody's accessibility theorem are key ingredients in this work. Readership Mathematicians interested in geometric group theory, shape theory, or cohomology of groups. Table of Contents  Geometric preliminaries
 Outline of the proof
 Dunwoody tracks and relative accessibility
 Basic lemmas
 Technical lemmas
 Proof of the halfspace lemma
 Proof of Theorem 3.3.
 Conclusion
