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Associated to every complete affine 3-manifold M with nonsolvable fundamental group is a noncompact hyperbolic surface S. We classify such complete affine structures when Sigma is homeomorphic to a three-holed sphere. In particular, for…

Differential Geometry · Mathematics 2011-07-12 Virginie Charette , Todd A. Drumm , William M. Goldman

When two smooth manifold bundles over the same base are fiberwise tangentially homeomorphic, the difference is measured by a homology class in the total space of the bundle. We call this the relative smooth structure class. Rationally and…

K-Theory and Homology · Mathematics 2012-04-10 Sebastian Goette , Kiyoshi Igusa , Bruce Williams

A regular fiber of the Seifert fibering of the Poincar\'e homology sphere admits a Dehn surgery to $L(2,1)\#L(3,2)\#L(5,4)$. We prove that this is the only knot in the Poincar\'e homology sphere with a surgery to a connected sum of more…

Geometric Topology · Mathematics 2021-01-06 Jacob Caudell

We consider complements of standard Seifert surfaces of special alternating links. On these handlebodies, we use Honda's method to enumerate those tight contact structures whose dividing sets are isotopic to the link, and find their number…

Geometric Topology · Mathematics 2020-03-25 Tamás Kálmán , Daniel V. Mathews

We consider a homology sphere $M_n(K_1,K_2)$ presented by two knots $K_1,K_2$ with linking number 1 and framing $(0,n)$. We call the manifold {\it Matsumoto's manifold}. We show that there exists no contractible bound of $M_n(T_{2,3},K_2)$…

Geometric Topology · Mathematics 2015-06-30 Motoo Tange

We calculate the Heegaard Floer homologies for three-manifolds obtained by plumbings of spheres specified by certain graphs. Our class of graphs is sufficiently large to describe, for example, all Seifert fibered rational homology spheres.…

Symplectic Geometry · Mathematics 2014-11-11 Peter Ozsvath , Zoltan Szabo

We define a differential graded algebra associated to Legendrian knots in Seifert fibered spaces with transverse contact structures. This construction is distinguished from other combinatorial realizations of contact homology invariants by…

Symplectic Geometry · Mathematics 2010-12-14 Joan E. Licata , Joshua M. Sabloff

We introduce generalized arrow diagrams and generalized Reidemeister moves for diagrams of links in Seifert fibered spaces. We give a presentation of the fundamental group of the link complement. As a corollary we are able to compute the…

Geometric Topology · Mathematics 2017-03-16 Boštjan Gabrovšek , Enrico Manfredi

We complete the classification of the smooth, closed, oriented 4-manifolds having Euler characteristic less than four and a horizontal handlebody decomposition of genus one. We use the classification result to find a large family of…

Geometric Topology · Mathematics 2025-08-20 Paolo Lisca , Andrea Parma

We construct an infinite family of knots in rational homology spheres with irreducible, non-fibered complements, for which every non-longitudinal filling is an L-space.

Geometric Topology · Mathematics 2016-01-20 Tye Lidman , Liam Watson

We give infinitely many examples of manifold-knot pairs (Y, J) such that Y bounds an integer homology ball, J does not bound a non-locally-flat PL-disk in any integer homology ball, but J does bound a smoothly embedded disk in a rational…

Geometric Topology · Mathematics 2021-07-20 Kristen Hendricks , Jennifer Hom , Matthew Stoffregen , Ian Zemke

We give examples of non-fibered hyperbolic knot complements in homology spheres that are not commensurable to fibered knot complements in homology spheres. In fact, we give many examples of knot complements in homology spheres with the…

Geometric Topology · Mathematics 2007-05-23 Danny Calegari , Nathan M. Dunfield

We corrected a few errors in the previous submission. These do not affect any of the topological conclusions of the earlier version. We have also included a few observations about the Casson invariant of the Brieskorn homology spheres.

dg-ga · Mathematics 2007-05-23 Liviu I. Nicolaescu

There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a…

Algebraic Geometry · Mathematics 2014-10-14 Alexander I. Suciu

We establish restrictions on Lagrangian embeddings of rational homology spheres into certain open symplectic manifolds, namely the (A_m) Milnor fibres of odd complex dimension. This relies on general considerations about equivariant objects…

Symplectic Geometry · Mathematics 2014-11-11 Paul Seidel

Let W -> X be a real smooth projective 3-fold fibred by rational curves. J. Koll\'ar proved that, if W(R) is orientable, then a connected component N of W(R) is essentially either a Seifert fibred manifold or a connected sum of lens spaces.…

Algebraic Geometry · Mathematics 2025-05-26 Fabrizio Catanese , Frederic Mangolte

The first part of this paper is a short review of the construction [dg-ga/9710001] of invariants of rational homology 3-spheres and knots in terms of configuration space integrals. The second part describes the relationship between the…

Geometric Topology · Mathematics 2007-05-23 Alberto S. Cattaneo

In this paper, we develop the theory for classifying all the geometric fibrations of compact, connected, flat $n$-orbifolds, over a 1-orbifold, up to affine equivalence. We apply our classification theory to classify all the geometric…

Geometric Topology · Mathematics 2020-05-08 John G. Ratcliffe , Steven T. Tschantz

In this paper we deal with Seifert fibre spaces, which are compact 3-manifolds admitting a foliation by circles. We give a combinatorial description for these manifolds in all the possible cases: orientable, non-orientable, closed, with…

Geometric Topology · Mathematics 2018-02-28 Alessia Cattabriga , Sergei Matveev , Michele Mulazzani , Timur Nasybullov

Given a rational homology sphere which bounds rational homology balls, we investigate the complexity of these balls as measured by the number of 1-handles in a handle decomposition. We use Casson-Gordon invariants to obtain lower bounds…

Geometric Topology · Mathematics 2017-11-27 Paolo Aceto , Marco Golla , Ana G. Lecuona