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1,169
Automorphic forms and rational homology 3-spheres
- GEOM. TOPOL
, 2006
"... We investigate a question of Cooper adjacent to the Virtual Haken Conjecture. Assuming certain conjectures in number theory, we show that there exist hyperbolic rational homology 3–spheres with arbitrarily large injectivity radius. These examples come from a tower of abelian covers of an explicit ar ..."
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Cited by 20 (4 self)
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We investigate a question of Cooper adjacent to the Virtual Haken Conjecture. Assuming certain conjectures in number theory, we show that there exist hyperbolic rational homology 3–spheres with arbitrarily large injectivity radius. These examples come from a tower of abelian covers of an explicit
RATIONAL SURGERY FORMULA FOR HABIRO–LE INVARIANTS OF RATIONAL HOMOLOGY 3–SPHERES
, 2006
"... Abstract. Habiro–Le invariants dominate sl2 Witten–Reshetikhin–Turaev invariants of rational homology 3–spheres at roots of unity of order coprime with the torsion. In this paper we give a formula for the Habiro–Le invariant of a rational homology 3–sphere obtained by rational surgery on a link in S ..."
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Abstract. Habiro–Le invariants dominate sl2 Witten–Reshetikhin–Turaev invariants of rational homology 3–spheres at roots of unity of order coprime with the torsion. In this paper we give a formula for the Habiro–Le invariant of a rational homology 3–sphere obtained by rational surgery on a link
On Finite Type 3-Manifold Invariants V: Rational Homology 3-Spheres
, 1995
"... . We introduce a notion of finite type invariants of oriented rational homology 3-spheres. We show that the map to finite type invariants of integral homology 3-spheres is one-to-one and deduce that the space of finite type invariants of rational homology 3-spheres is a filtered commutative algeb ..."
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Cited by 6 (2 self)
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. We introduce a notion of finite type invariants of oriented rational homology 3-spheres. We show that the map to finite type invariants of integral homology 3-spheres is one-to-one and deduce that the space of finite type invariants of rational homology 3-spheres is a filtered commutative
On perturbative PSU(n) invariants of rational homology 3-spheres, Topology
"... Abstract. We construct power series invariants of rational homology 3-spheres from quantum PSU(n)-invariants. The power series can be regarded as perturbative invariants corresponding to the contribution of the trivial connection in the hypothetical Witten’s integral. This generalizes a result of Oh ..."
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Cited by 12 (6 self)
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Abstract. We construct power series invariants of rational homology 3-spheres from quantum PSU(n)-invariants. The power series can be regarded as perturbative invariants corresponding to the contribution of the trivial connection in the hypothetical Witten’s integral. This generalizes a result
A UNIFIED QUANTUM SO(3) INVARIANT FOR RATIONAL HOMOLOGY 3–SPHERES
, 801
"... Abstract. Given a rational homology 3–sphere M with |H1(M, Z) | = b and a link L inside M, colored by odd numbers, we construct a unified invariant IM,L belonging to a modification of the Habiro ring where b is inverted. Our unified invariant dominates the whole set of the SO(3) Witten–Reshetikhin– ..."
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Cited by 4 (3 self)
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Abstract. Given a rational homology 3–sphere M with |H1(M, Z) | = b and a link L inside M, colored by odd numbers, we construct a unified invariant IM,L belonging to a modification of the Habiro ring where b is inverted. Our unified invariant dominates the whole set of the SO(3) Witten
Unified SO(3) quantum invariant for rational homology 3-spheres, preprint
"... Abstract. Let M be a rational homology 3–sphere with |H1(M, Z) | = b. For any odd divisor c of b, we construct a unified invariant IM,c lying in a cyclotomic completion of a certain polynomial ring, which dominates Witten–Reshetikhin–Turaev SO(3) invariants of M at all roots of unity whose order r ..."
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Cited by 1 (0 self)
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Abstract. Let M be a rational homology 3–sphere with |H1(M, Z) | = b. For any odd divisor c of b, we construct a unified invariant IM,c lying in a cyclotomic completion of a certain polynomial ring, which dominates Witten–Reshetikhin–Turaev SO(3) invariants of M at all roots of unity whose order r
Topology and its Applications 101 (2000) 143–148 Free actions of finite groups on rational homology 3-spheres
, 1997
"... We show that any finite group can act freely on a rational homology 3-sphere. Ó 2000 Elsevier Science B.V. All rights reserved. ..."
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We show that any finite group can act freely on a rational homology 3-sphere. Ó 2000 Elsevier Science B.V. All rights reserved.
LINKING NUMBERS IN RATIONAL HOMOLOGY 3-SPHERES, CYCLIC BRANCHED COVERS AND INFINITE CYCLIC COVERS
, 2001
"... We study the linking numbers in a rational homology 3-sphere and in the infinite cyclic cover of the complement of a knot. They take values in Q and in Q(Z[t,t −1]) respectively, where Q(Z[t,t −1]) denotes the quotient field of Z[t,t −1]. It is known that the modulo-Z linking number in the rational ..."
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Cited by 3 (1 self)
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We study the linking numbers in a rational homology 3-sphere and in the infinite cyclic cover of the complement of a knot. They take values in Q and in Q(Z[t,t −1]) respectively, where Q(Z[t,t −1]) denotes the quotient field of Z[t,t −1]. It is known that the modulo-Z linking number in the rational
Free Actions of Finite Groups on Rational Homology 3-Spheres
, 1996
"... Introduction. The purpose of this note is to prove the following: Theorem 1.1 Let G be a finite group. Then there is a rational homology S 3 on which G acts freely. That any finite group acts freely on some closed 3-manifold is easy to arrange: There are many examples of closed 3-manifolds whos ..."
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Cited by 12 (0 self)
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Introduction. The purpose of this note is to prove the following: Theorem 1.1 Let G be a finite group. Then there is a rational homology S 3 on which G acts freely. That any finite group acts freely on some closed 3-manifold is easy to arrange: There are many examples of closed 3-manifolds
Results 1 - 10
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