## Low-dimensional and Symplectic TopologyEvery eight years since 1961, the University of Georgia has hosted a major international topology conference aimed at disseminating important recent results and bringing together researchers at different stages of their careers. This volume contains the proceedings of the 2009 conference, which includes survey and research articles concerning such areas as knot theory, contact and symplectic topology, 3-manifold theory, geometric group theory, and equivariant topology. Among other highlights of the volume, a survey article by Stefan Friedl and Stefano Vidussi provides an accessible treatment of their important proof of Taubes' conjecture on symplectic structures on the product of a 3-manifold and a circle, and an intriguing short article by Dennis Sullivan opens the door to the use of modern algebraic-topological techniques in the study of finite-dimensional models of famously difficult problems in fluid dynamics. Continuing what has become a tradition, this volume contains a report on a problem session held at the conference, discussing a variety of open problems in geometric topology. |

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### Contents

Subgroups and quotients of automorphism groups of RAAGs | 9 |

Abelian ρinvariants of iterated torus knots | 29 |

A surgical perspective on quasialternating links | 39 |

Thurston norm and cosmetic surgeries | 53 |

On the relative Giroux correspondence | 65 |

A note on the support norm of a contact structure | 79 |

Topological properties of Reeb orbits on boundaries of starshaped domains | 89 |

Twisted Alexander polynomials and fibered 3manifolds | 111 |

Displacing Lagrangian toric fibers via probes | 131 |

Equivariant Bredon cohomology and ˇCech hypercohomology | 161 |

Sphere recognition lies in | 183 |

Open problems in geometric topology | 215 |

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3-manifolds abelian Alexander polynomial algebra algorithm automorphism boundary regular cohomology complex components compute connect sum contact structure contains convex Corollary deﬁned Definition Dehn denote disjoint displaceable dividing set edge embedded epimorphism equivariant facial curves fibered Figure ﬁnite finite solvable ﬁrst Floer homology follows Heegaard diagram Heegaard Floer homology hence homeomorphic homotopy induced integral intersection invariant isomorphism isotopy Lemma lens space lk[v Math Mathematics normal bundle normal surface normal two-sphere obtained open book decomposition partial open book polytope presheaf probes Problem proof of Theorem Proposition quasi-alternating links Reeb orbit residually finite Section Seifert self-intersection number simplicial smooth star Ewald condition subgroup Suppose surgery sutured manifold symplectic tangle Theorem 1.1 three-manifold three-sphere Thurston norm tight contact structure tightening disk topology torus knot transverse orientation triangulation trivialization twisted Alexander polynomials two-fold branched cover vector vertex vertices