The boundary manifold of a complex line arrangement

We study the topology of the boundary manifold of a line arrangement in CP^2, with emphasis on the fundamental group G and associated invariants. We determine the Alexander polynomial Delta(G), and more generally, the twisted Alexander polynomial associated to the abelianization of G and an arbitrary complex representation. We give an explicit description of the unit ball in the Alexander norm, and use it to analyze certain Bieri-Neumann-Strebel invariants of G. From the Alexander polynomial, we also obtain a complete description of the first characteristic variety of G. Comparing this with the corresponding resonance variety of the cohomology ring of G enables us to characterize those arrangements for which the boundary manifold is formal.Comment: This is the version published by Geometry & Topology Monographs on 22 February 200

Cell decomposition of some unitary group Rapoport-Zink spaces

In this paper we study the $p$-adic analytic geometry of the basic unitary group Rapoport-Zink spaces \M_K with signature $(1,n-1)$. Using the theory of Harder-Narasimhan filtration of finite flat groups developed by Fargues in \cite{F2},\cite{F3}, and the Bruhat-Tits stratification of the reduced special fiber \M_{red} defined by Vollaard-Wedhorn in \cite{VW}, we find some relatively compact fundamental domain \D_K in \M_K for the action of G(\Q_p)\times J_b(\Q_p), the product of the associated $p$-adic reductive groups, and prove that \M_K admits a locally finite cell decomposition. By considering the action of regular elliptic elements on these cells, we establish a Lefschetz trace formula for these spaces by applying Mieda's main theorem in \cite{Mi2}.Comment: some minor errors are corrected; to appear in Math. An

Rigidity of infinitesimal momentum maps

In this paper we prove rigidity theorems for Poisson Lie group actions on Poisson manifolds. In particular, we prove that close infinitesimal momentum maps associated to Poisson Lie group actions are equivalent using a normal form theorem for SCI spaces. When the Poisson structure of the acted manifold is integrable, this yields rigidity also for lifted actions to the symplectic groupoid.Comment: 16 page

Rigidity of infinitesimal momentum maps

In this paper we prove rigidity theorems for Poisson Lie group actions on Poisson manifolds. In particular, we prove that close infinitesimal momentum maps associated to Poisson Lie group actions are equivalent using a normal form theorem for SCI spaces. When the Poisson structure of the acted manifold is integrable, this yields rigidity also for lifted actions to the symplectic groupoid.Peer ReviewedPostprint (updated version