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18
Mixed 3manifolds are virtually special
, 2012
"... Abstract. LetM be a compact oriented irreducible 3–manifold which is neither a graph manifold nor a hyperbolic manifold. We prove that pi1M is virtually special. 1. ..."
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Cited by 17 (2 self)
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Abstract. LetM be a compact oriented irreducible 3–manifold which is neither a graph manifold nor a hyperbolic manifold. We prove that pi1M is virtually special. 1.
A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4manifolds
 J. Eur. Math. Soc
"... Abstract. In this paper we show that given any 3manifold N and any nonfibered class in H 1 (N ; Z) there exists a representation such that the corresponding twisted Alexander polynomial is zero. This is obtained by extending earlier work of the authors, together with results of Agol and Wise on se ..."
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Cited by 16 (7 self)
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Abstract. In this paper we show that given any 3manifold N and any nonfibered class in H 1 (N ; Z) there exists a representation such that the corresponding twisted Alexander polynomial is zero. This is obtained by extending earlier work of the authors, together with results of Agol and Wise on separability of 3manifold groups. This result allows us to completely classify symplectic 4manifolds with a free circle action, and to determine their symplectic cones.
KÄHLER GROUPS, QUASIPROJECTIVE GROUPS, AND 3MANIFOLD GROUPS
 JOURNAL OF THE LONDON MATHEMATICAL SOCIETY
, 2014
"... We prove two results relating 3manifold groups to fundamental groups occurring in complex geometry. Let N be a compact, connected, orientable 3manifold. If N has nonempty, toroidal boundary, and π1(N) is a Kähler group, then N is the product of a torus with an interval. On the other hand, if N ..."
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Cited by 4 (2 self)
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We prove two results relating 3manifold groups to fundamental groups occurring in complex geometry. Let N be a compact, connected, orientable 3manifold. If N has nonempty, toroidal boundary, and π1(N) is a Kähler group, then N is the product of a torus with an interval. On the other hand, if N has either empty or toroidal boundary, and π1(N) is a quasiprojective group, then all the prime components of N are graph manifolds.
SPLITTINGS OF KNOT GROUPS
, 2014
"... Let K be a knot of genus g. If K is fibered, then it is well known that the knot group pi(K) splits only over a free group of rank 2g. We show that if K is not fibered, then pi(K) splits over nonfree groups of arbitrarily large rank. Furthermore, if K is not fibered, then pi(K) splits over every fr ..."
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Cited by 2 (2 self)
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Let K be a knot of genus g. If K is fibered, then it is well known that the knot group pi(K) splits only over a free group of rank 2g. We show that if K is not fibered, then pi(K) splits over nonfree groups of arbitrarily large rank. Furthermore, if K is not fibered, then pi(K) splits over every free group of rank at least 2g. However, pi(K) cannot split over a group of rank less than 2g. The last statement is proved using the recent results of Agol, Przytycki–Wise and Wise.
Residual finiteness growths of virtually special groups
"... Abstract. Let G be a virtually special group. Then the residual finiteness growth of G is at most linear. This result cannot be found by embedding G into a special linear group. Indeed, the special linear group SLk(Z), for k> 2, has residual finiteness growth nk−1. ..."
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Cited by 1 (0 self)
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Abstract. Let G be a virtually special group. Then the residual finiteness growth of G is at most linear. This result cannot be found by embedding G into a special linear group. Indeed, the special linear group SLk(Z), for k> 2, has residual finiteness growth nk−1.