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Twisted Alexander polynomials detect fibered 3manifolds
 Monopoles and ThreeManifolds, New Mathematical Monographs (No. 10), Cambridge University Press. , Knots, sutures and excision
"... Abstract. A classical result in knot theory says that for a fibered knot the Alexander polynomial is monic and that the degree equals twice the genus of the knot. This result has been generalized by various authors to twisted Alexander polynomials and fibered 3–manifolds. In this paper we show that ..."
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Cited by 40 (11 self)
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Abstract. A classical result in knot theory says that for a fibered knot the Alexander polynomial is monic and that the degree equals twice the genus of the knot. This result has been generalized by various authors to twisted Alexander polynomials and fibered 3–manifolds. In this paper we show that the conditions on twisted Alexander polynomials are not only necessary but also sufficient for a 3–manifold to be fibered. By previous work of the authors this result implies that if a manifold of the form S 1 × N 3 admits a symplectic structure, then N fibers over S 1. In fact we will completely determine the symplectic cone of S 1 × N in terms of the fibered faces of the Thurston norm ball of N. 1.
Twisted Alexander polynomials and fibered 3–manifolds
 PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS
"... In a series of papers the authors proved that twisted Alexander polynomials detect fibered 3manifolds, and they showed that this implies that a closed 3–manifold N is fibered if and only if S1 × N is symplectic. In this note we summarize some of the key ideas of the proofs. We also give new eviden ..."
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Cited by 5 (4 self)
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In a series of papers the authors proved that twisted Alexander polynomials detect fibered 3manifolds, and they showed that this implies that a closed 3–manifold N is fibered if and only if S1 × N is symplectic. In this note we summarize some of the key ideas of the proofs. We also give new evidence to the conjecture that if M is a symplectic 4–manifold with a free S1–action, then the orbit space is fibered.
Conjugacy pseparability of rightangled Artin groups and applications
, 2013
"... We prove that every subnormal subgroup of ppower index in a rightangled Artin group is conjugacy pseparable. As an application, we prove that every rightangled Artin group is conjugacy separable in the class of torsionfree nilpotent groups. As another application, we prove that the outer automo ..."
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Cited by 2 (0 self)
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We prove that every subnormal subgroup of ppower index in a rightangled Artin group is conjugacy pseparable. As an application, we prove that every rightangled Artin group is conjugacy separable in the class of torsionfree nilpotent groups. As another application, we prove that the outer automorphism group of a rightangled Artin group is virtually residually pfinite. We also prove that the Torelli groupofarightangledArtingroupisresiduallytorsionfreenilpotent, hence residually pfinite and biorderable. 1
Residual properties of 3manifold groups I: Fibered and hyperbolic 3manifolds
, 2010
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Residual Properties of Fibered and Hyperbolic 3manifolds
, 2011
"... Let p be a prime. In this paper, we classify the geometric 3– manifolds whose fundamental groups are virtually residually p. Let M = M 3 be a virtually fibered 3manifold. We prove that π1(M) is always virtually residually p. Using recent work of Wise, we prove that every hyperbolic 3–manifold is ei ..."
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Let p be a prime. In this paper, we classify the geometric 3– manifolds whose fundamental groups are virtually residually p. Let M = M 3 be a virtually fibered 3manifold. We prove that π1(M) is always virtually residually p. Using recent work of Wise, we prove that every hyperbolic 3–manifold is either closed or virtually fibered and hence has a virtually residually p fundamental group. We then investigate some conditions under which the fundamental group of M is virtually residually torsion–free nilpotent.