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Abstract. As a generalization of a classical result on the Alexander polynomial for fibered knots, we show in this paper that the Reidemeister torsion associated to a certain representation detects fiberedness of knots in the three sphere. Mathematics Subject Classification (2000). Primary 57M25; Secondary 57M05.

We describe low dimensional homology groups of Diff δ + S 1 in terms of Haefliger's classifying space BΓ 1 by applying a theorem of Thurston. Then we consider the question whether some power of the rational Euler class vanishes for real analytic flat S 1 -bundles. We show that if it occurs, then the homology group of Diff ω,δ + S 1 should contain two kinds of many torsion classes which vanish in Diff δ + S 1 . This is an informal note on our discussions about the above question (see Remark 1.17).Theorem 1.1 (Thurston [23]). Let h : B Diff δ + S 1 × S 1 → BΓ 1 be the classifying map for the flat S 1 -product over B Diff δ + S 1 . Then its adjoint mappingBy making use of this theorem, we obtain the following results.

′ is a surjective homomorphism, we prove that the twisted Alexander polynomial of G is divisible by the twisted Alexander polynomial of G ′ . As an application, we show non-existence of surjective homomorphism between certain knot groups.