相关论文: Alexander and Thurston norms of fibered 3-manifold…

We introduce and investigate the notion of (strong) $K^n_G$-manifolds, where $G$ is an abelian group. One of the result related to that notion (Theorem 3.4) implies the following partial answer to the Bing-Borsuk problem \cite{bb}, whether…

The triangulation complexity of a closed orientable 3-manifold is the minimal number of tetrahedra in any triangulation of the manifold. The main theorem of the paper gives upper and lower bounds on the triangulation complexity of any…

In this paper we present a sequence of link invariants, defined from twisted Alexander polynomials, and discuss their effectiveness in distinguish knots. In particular, we recast and extend by geometric means a recent result of Silver and…

We prove a geometric refinement of Alexander duality for certain 2-complexes, the so-called gropes, embedded into 4-space. This refinement can be roughly formulated as saying that 4-dimensional Alexander duality preserves the disjoint Dwyer…

In three dimensions, a `master theory' for all Thurston geometries requires imaginary flux. However, these geometries can be obtained from physical three-dimensional theories with various additional scalar fields, which can be interpreted…

Let the complexity of a closed manifold M be the minimal number of simplices in a triangulation of M. Such a quantity is clearly submultiplicative with respect to finite coverings, and by taking the infimum on all finite coverings of M…

By a recent result of Livingston, it is known that if a knot has a prime power branched cyclic cover that is not a homology sphere, then there is an infinite family of non-concordant knots having the same Seifert form as the knot. In this…

We study the twisted Alexander polynomial $\Delta_{K,\rho}$ of a knot $K$ associated to a non-abelian representation $\rho$ of the knot group into $SL_2(\BC)$. It is known for every knot $K$ that if $K$ is fibered, then for every…

In this short note, we show that the twisted Alexander polynomial associated to a parabolic SL(2,C)-representation detects genus and fibering of the twist knots. As a corollary, a conjecture of Dunfield, Friedl and Jackson is proved for the…

To any complex algebraic variety endowed with a morphism to a complex affine torus we associate multivariable cohomological Alexander modules, and define natural mixed Hodge structures on their maximal Artinian submodules. The key…

We give a brief summary of some of our work and our joint work with Stephan Tillmann on solving Thurston's equation and Haken equation on triangulated 3-manifolds in this paper. Several conjectures on the existence of solutions to…

We study the Newton polytopes of determinants of square matrices defined over rings of twisted Laurent polynomials. We prove that such Newton polytopes are single polytopes (rather than formal differences of two polytopes); this result can…

The following criterion is proved in this paper. If the Alexander polynomial of a knot $K\subset S^3$ has a zero of odd order on the complex unit circle, then there exists a continuous family of irreducible representations…

Let $Y_-$ and $Y_+$ be two compact 3-manifolds with empty or toroidal boundary. A 4-dimensional ribbon homology cobordism is a homologically trivial cobordism built with 1-handles and 2-handles. In this note, following the work of Friedl…

We present an algorithm for the following problem. Given a triangulated 3-manifold M and a (possibly non-simple) closed curve on the boundary of M, decide whether this curve is contractible in M. Our algorithm runs in space polynomial in…

We define a norm on the homology of a foliated manifold, which refines and majorizes the usual Gromov norm on homology. This norm depends in an upper semi-continuous way on the underlying foliation, in the geometric topology, and can…

An interesting question in symplectic topology, which was posed by C. H. Taubes, concerns the topology of closed (i.e. compact and without boundary) connected oriented three dimensional manifolds whose product with a circle admits a…

This note is an elaboration of the ideas and intuitions of Grothendieck and Weil concerning the "arithmetic topology". Given 3-dimensional manifold M fibering over the circle we introduce an real quadratic number field K with discriminant…

We answer Hubbard's question on determining the Thurston equivalence class of ``twisted rabbits'', i.e. images of the ``rabbit'' polynomial under n-th powers of the Dehn twists about its ears. The answer is expressed in terms of the 4-adic…

Given two compact n-dimensional manifolds in the smooth, piecewise linear or topological categories, basic results of B. Mazur and others give simple criteria for determining whether their products with Euclidean spaces of sufficiently…