17 citations · 75 across the 24 of their papers we have counts for
14 papers · 1 filter
Spectral sequences, Massey products and homology of covering spaces
Yongqiang Liu, Laurentiu Maxim, Botong Wang
We revisit the equivariant spectral sequence considered by Papadima-Suciu, and show that all its differentials are computed by higher order Massey products. As a first application,…
Maximal twisted Betti numbers of complex hyperplane arrangement complements
Yongqiang Liu, Laurentiu Maxim, Botong Wang
We show that the Betti numbers of a local system on the complement of an essential complex hyperplane arrangement are maximized precisely when the local system is constant. This re…
Cohomology of -local systems on complex hyperplane arrangement complements
Yongqiang Liu, Laurenţiu Maxim, Botong Wang
We prove a Cohen-Dimca-Orlik type theorem for rank one -local systems on complex hyperplane arrangement complements. This settles a recent conjecture of S. Sugawara.
Length of Perverse Sheaves on Hyperplane Arrangements
Nero Budur, Yongqiang Liu
In this article we address the length of perverse sheaves arising as direct images of rank one local systems on complements of hyperplane arrangements. In the case of a cone over a…
Perverse sheaves on semi-abelian varieties -- a survey of properties and applications
Yongqiang Liu, Laurentiu Maxim, Botong Wang
We survey recent developments in the study of perverse sheaves on semi-abelian varieties. As concrete applications, we discuss various obstructions on the homotopy type of complex…
Mellin transformation, propagation, and abelian duality spaces
Yongqiang Liu, Laurentiu Maxim, Botong Wang
For arbitrary field coefficients , we show that -perverse sheaves on a complex affine torus satisfy the so-called propagation package, i.e., the generic van…
Milnor and Tjurina numbers for a hypersurface germ with isolated singularity
Yongqiang Liu
Assume that is an analytic function germ at the origin with only isolated singularity. Let and be the corresponding Milnor and Tjuri…
Generic vanishing for semi-abelian varieties and integral Alexander modules
Yongqiang Liu, Laurentiu Maxim, Botong Wang
We revisit generic vanishing results for perverse sheaves with any field coefficients on a complex semi-abelian variety, and indicate several topological applications. In particula…
Topology of subvarieties of complex semi-abelian varieties
Yongqiang Liu, Laurentiu Maxim, Botong Wang
We use the non-proper Morse theory of Palais-Smale to investigate the topology of smooth closed subvarieties of complex semi-abelian varieties, and that of their infinite cyclic co…
Spectral pairs, Alexander modules, and boundary manifolds
Yongqiang Liu, Laurentiu Maxim
Let $f: \CN \rightarrow \C $ be a reduced polynomial map, with , $\U=\CN \setminus D$ and boundary manifold $M=\partial \U$. Assume that is transversal at infinity…
The total Milnor number of the weighted-Le-Yomdin-at-infinity polynomial
Yongqiang Liu
We give a concrete formula for the total Milnor number of the weighted-Le-Yomdin-at-infinity polynomial in most of the interesting cases. As an application, we give a description o…
Characteristic Varieties of Hypersurface Complements
Yongqiang Liu, Laurentiu Maxim
We give divisibility results for the (global) characteristic varieties of hypersurface complements expressed in terms of the local characteristic varieties at points along one of t…
Reidemeister Torsion, Peripheral Complex, and Alexander Polynomials of Hypersurface Complements
Yongqiang Liu, Laurentiu Maxim
Let $f:\CN \rightarrow \C $ be a polynomial, which is transversal (or regular) at infinity. Let $\U=\CN\setminus f^{-1}(0)$ be the corresponding affine hypersurface complement. By…
Nearby Cycles and Alexander Modules of Hypersurface Complements
Yongqiang Liu
Let $f:\CN \rightarrow \C $ be a polynomial map, which is transversal at infinity. Using Sabbah's specialization complex, we give a new description of the Alexander modules of the…