Warren Dicks,
Groups, trees and projective modules.
Lecture Notes in Mathematics
790.
Springer-Verlag, Berlin, 1980. ix + 127pp.
Addenda
October 4, 2004.
The construction described in Preparatory Remarks II.4.1 was suggested
by a construction
of Ian Chiswell, which was in turn suggested by the "binding ties" of
John R. Stallings,
A
topological proof of Grushko's theorem on free products.
Math.
Z. 90 (1965), 1-8.
The construction in question was given the apt name "folding" in
Section 3.2 of
John R.
Stallings,
Topology
of finite graphs.
Invent.
Math. 71 (1983), 551-565.
where many other useful properties of folding were described.
The proof of Theorem II.4.2 was suggested by a proof by Ian
Chiswell, which was in turn
suggested by the binding-ties proof of John Stallings. Our proof
was later expanded in
John R.
Stallings,
Foldings
of G-trees.
pp. 355-368
of Arboreal Group Theory (Berkeley, CA, 1988),
Math.
Sci. Res. Inst. Publ. 19, Springer, New York, 1991.
Theorem III.1.4 answers, in the affirmative, problem B11, p. 374, of
C. T. C. Wall (editor)
Homological group theory (Proc. Sympos., Durham,
1977),
London Math. Soc. Lecture Note Ser., 36.
Cambridge Univ. Press, Cambridge, 1979.
Errata
October 28, 2005.
Page 4, last line. For what we call "star(v)", the standard notation
is "link(v)".
Page 32, second last line. Change "[g*,e] =" to "[g*,e]
\subseteq".
Page 45. Replace the final sentence with the following:
"There is an obvious
surjective graph morphism X' -> X, and our hypotheses
ensure that it is injective on edges, so it is an isomorphism,
so H_y = G_y for all y \in Y."
Page 62, line 11. Change "lies in a different" to "is a".
Page 104, 10th last line. Change "R[{\sigma_{uG}
| u \in U}]" to "\sum_{u\in U} R \sigma_{uG}".
Page 109, line 6. After "{v \in V(X) | 1 \ne
G_v \subseteq H}" insert "\cup {v_H}".
Page 109, line 7. After "subtree of X," insert
"since it is closed under paths to v_H,"
Return to Warren Dicks' publications.