相关论文: Guts determine the leading coefficients of $L^2$-A…

We give upper and lower bounds on the leading coefficients of the $L^2$-Alexander torsions of a $3$-manifold $M$ in terms of hyperbolic volumes and of relative $L^2$-torsions of sutured manifolds obtained by cutting $M$ along certain…

We introduce $L^2$-Alexander torsions for 3-manifolds, which can be viewed as a generalization of the $L^2$-Alexander polynomial of Li--Zhang. We state the $L^2$-Alexander torsions for graph manifolds and we partially compute them for…

For an irreducible orientable compact $3$-manifold $N$ with empty or incompressible toral boundary, the full $L^2$--Alexander torsion $\tau^{(2)}(N,\phi)(t)$ associated to any real first cohomology class $\phi$ of $N$ is represented by a…

We construct an invariant called guts for second homology classes in irreducible 3-manifolds with toral boundary and non-degenerate Thurston norm. We prove that the guts of second homology classes in each Thurston cone are invariant under a…

We obtain generalizations of some results of Turaev relating leading order terms of the Turaev torsion of closed, oriented, connected 3-manifolds to certain ``determinants'' derived from cohomology operations such as the alternate trilinear…

Let M be an oriented irreducible 3-manifold with infinite fundamental group and empty or toroidal boundary. Consider any element \phi in the first cohomology of M with integral coefficients. Then one can define the \phi-twisted L^2-torsion…

For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable 3-manifolds, including the ``piecewise geometric'' ones in the sense of…

We show that L\"uck's conjecture on torsion growth in homology implies that two 3-manifolds have equal volume if the fundamental groups have the same set of finite quotients.

We show that the $L^2$-Alexander torsion of a 3-manifold is symmetric. This can be viewed as a generalization of the symmetry of the Alexander polynomial of a knot.

Every element in the first cohomology group of a 3--manifold is dual to embedded surfaces. The Thurston norm measures the minimal `complexity' of such surfaces. For instance the Thurston norm of a knot complement determines the genus of the…

We assign to a finite $CW$-complex and an element in its first cohomology group a twisted version of the $L^2$-Euler characteristic and study its main properties. In the case of an irreducible orientable $3$-manifold with empty or toroidal…

We study when the Thurston norm is detected by twisted Alexander polynomials associated to representations of the 3-manifold group to SL(2, C). Specifically, we show that the hyperbolic torsion polynomial determines the genus for a large…

We investigate the local deformation space of 3-dimensional cone-manifold structures of constant curvature $\kappa \in \{-1,0,1\}$ and cone-angles $\leq \pi$. Under this assumption on the cone-angles the singular locus will be a trivalent…

In this paper we consider the cohomology of a closed arithmetic hyperbolic 3-manifold with coefficients in the local system defined by the even symmetric powers of the standard representation of SL(2,C). The cohomology is defined over the…

We give definitions of cohomology determinants for compact, connected, orientable 3-manifolds. We also give formulae relating cohomology determinants before and after gluing a solid torus along a torus boundary component. Cohomology…

Let $L$ be a closed, orientable, monotone Lagrangian 3-manifold of a symplectic manifold $(M, \omega)$, for which there exists a local system such that the corresponding Lagrangian quantum homology vanishes. We show that its cohomology ring…

For a manifold with an affine connection, we prove formulas which infinitesimally quantify the gap in a certain naturally defined open geodesic quadrilateral associated to a pair of tangent vectors $u$, $v$ at a point of the manifold. We…

Suppose $\bar{M}$ is a compact connected odd-dimensional manifold with boundary, whose interior $M$ comes with a complete hyperbolic metric of finite volume. We will show that the $L^2$-topological torsion of $\bar{M}$ and the…

The twisted torsion of a 3-manifold is well-known to be zero whenever the corresponding twisted Alexander module is non-torsion. Under mild extra assumptions we introduce a new twisted torsion invariant which is always non-zero. We show how…

We calculate the $L^2$-Alexander torsion for Seifert fiber spaces and graph manifolds in terms of the Thurston norm.