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CORRECTION TO ‘K-THEORY OFVIRTUALLY POLY-SURFACE GROUPS’arXiv:math.GT/0307159 v2 18 Aug 2004S. K. RoushonAugust 18, 2004Abstract. In this note we point out an error in the above paper and refer to somepapers where this error is corrected and a more general theorem is proved.In this note ‘FIC’ stands for the Fibered Isomorphism Conjecture of Farrell andJones corresponding to the pseudoisotopy functor (see [FJ]).In the proof of the main lemma of [R1] we found some filtration of the surface ˜Fwhich is preserved by the diffeomorphism f and used this filtration to find a filtrationof the mapping torus M f of f by compact submanifolds with incompressibletori boundary. Recall that ˜F was the covering of the surface F corresponding tothe commutator subgroup of π 1 (F) and f : ˜F → ˜F was a lift of a diffeomorphismg : F → F. Also recall that the main lemma of [R1] says that the FIC is truefor π 1 (M) where M is the mapping torus of a diffeomorphism of F. The proof ofthe existence of the above filtration of M f , we sketched in [R1] is incorrect. In theproof of the main lemma of [R2] we show that some regular finite sheeted cover ofM f admits a filtration of the required type provided g satisfies certain conditions.For general g we prove the main lemma of [R1] in [R3] assuming that the FIC istrue for B-groups. By definition a B-group contains a finite index subgroup isomorphicto the fundamental group of a compact irreducible 3-manifold with nonemptyincompressible boundary so that each boundary component is a surface of genus≥ 2. Finally we refer to [[R4], corollary 1.1] where we prove that the FIC is truefor B-groups. This completes the proof of the main lemma of [R1].1991 Mathematics Subject Classification. Primary: 19B28, 19A31, 20F99, 19D35. Secondary:19J10.Key words and phrases. Strongly poly-surface groups, Whitehead group, fibered isomorphismconjecture, negative K-groups.1

2 S. K. ROUSHONRecall that the strongly poly-surface groups ([[R1], definition]) were defined in[R1] and the FIC was proved for any virtually strongly poly-surface group ([[R1],main theorem]). We generalized this notion and defined weak strongly poly-surfacegroups (see [[R4], definition 1.1]) and in [[R4], theorem 1.2] the FIC is proved forany virtually weak strongly poly-surface group.Also we should point out that in this situation the proof of proposition 2.3 of [R1]needs a slightly elaborate argument. This proof is now contained in the proof of themain theorem of [R3] and stated in corollary 3.5 of [R3]. Recall that proposition2.3 says that the FIC is true for the fundamental group of a 3-manifold which hasa finite sheeted cover fibering over the circle.References[FJ] Farrell, F.T. and Jones, L.E., Isomorphism conjectures in algebraic K-theory, J. Amer.Math. Soc. 6 (1993), 249–297.[R1] S.K. Roushon, K-theory of virtually poly-surface groups, Algebr. Geom. Topol. 3 (2003),103–116.[R2] , Fibered isomorphism conjecture for complex manifolds, preprint, math.GT/0209119,revised on March 2004, submitted.[R3] , The Farrell-Jones isomorphism conjecture for 3-manifold groups, preprint, math.KT/0405211,submitted.[R4] , The isomorphism conjecture for 3-manifold groups and K-theory of virtually polysurfacegroups, preprint, math.KT/0408243.School of Mathematics, Tata Institute, Homi Bhabha Road, Mumbai 400 005, India.E-mail address: roushon@math.tifr.res.inURL: http://www.math.tifr.res.in/~ roushon/paper.html