Aspherical manifolds, Mellin transformation and a question of Bobadilla–Kollár

In their paper from 2012, Bobadilla and Kollár studied topological conditions which guarantee that a proper map of complex algebraic varieties is a topological or differentiable fibration. They also asked whether a certain finiteness property on the relative covering space can imply that a proper map is a fibration. In this paper, we answer positively the integral homology version of their question in the case of abelian varieties, and the rational homology version in the case of compact ball quotients. We also propose several conjectures in relation to the Singer–Hopf conjecture in the complex projective setting.

Effect Evaluation of Spatial Characteristics on Map Matching-Based Indoor Positioning

Map-matching is a popular method that uses spatial information to improve the accuracy of positioning methods. The performance of map matching methods is closely related to spatial characteristics. Although several studies have demonstrated that certain map matching algorithms are affected by some spatial structures (e.g., parallel paths), they focus on the analysis of single map matching method or few spatial structures. In this study, we explored how the most commonly-used four spatial characteristics (namely forks, open spaces, corners, and narrow corridors) affect three popular map matching methods, namely particle filtering (PF), hidden Markov model (HMM), and geometric methods. We first provide a theoretical analysis on how spatial characteristics affect the performance of map matching methods, and then evaluate these effects through experiments. We found that corners and narrow corridors are helpful in improving the positioning accuracy, while forks and open spaces often lead to a larger positioning error. We hope that our findings are helpful for future researchers in choosing proper map matching algorithms with considering the spatial characteristics.

Site selection criteria for temporary sheltering in urban environment

Purpose The inevitable occurrence of natural disasters and crisis arising from them causes a lot of losses globally, particularly in disaster-prone countries such as Iran. One of the main issues considered by organizations involved in crisis management is the selection of suitable sites for temporary sheltering for disaster victims. This study aims to choose safe places to establish temporary sheltering in urban environment. Design/methodology/approach Initially, relevant factors are identified by reviewing literature and through consultation with disaster experts. Next, the important layers were collected and analytical hierarchy process was used to assess the criteria weights based on their effectiveness on selection of safe sites for temporary sheltering. Finally, for integrating layers of factors, overlay and fuzzy models were used in Geographic Information System (GIS) environment, and subsequently, a proper map was prepared and suitable areas were identified. Findings 7 main criteria and 19 sub-criteria were selected to provide safe places for temporary sheltering. The results of fuzzy model in this study provide more accurate and limited safe areas for temporary sheltering when compared to index overlay model. Originality/value The results of this study will help decision-makers and local and regional managers to reduce the vulnerability of at-risk communities in urban environments. Moreover, choosing appropriate places for temporary shelters would help build community disaster resilience according to these criteria.

Toric Geometry ofSL2(ℂ) Free Group Character Varieties from Outer Space

Culler and Vogtmann defined a simplicial spaceO(g), calledouter space, to study the outer automorphism group of the free groupFg. Using representation theoretic methods, we give an embedding ofO(g) into the analytification of X(Fg,SL2(ℂ)), theSL2(ℂ) character variety ofFg, reproving a result of Morgan and Shalen. Then we show that every pointvcontained in a maximal cell ofO(g) defines a flat degeneration of X(Fg,SL2(ℂ)) to a toric varietyX(PΓ). We relate X(Fg,SL2(ℂ)) andX(v) topologically by showing that there is a surjective, continuous, proper map Ξv:X(Fg,SL2(ℂ)) →X(v). We then show that this map is a symplectomorphism on a dense open subset of X(Fg, SL2(ℂ)) with respect to natural symplectic structures on X(Fg, SL2(ℂ)) andX(v). In this way, we construct an integrable Hamiltonian system in X(Fg, SL2(ℂ)) for each point in a maximal cell ofO(g), and we show that eachvdefines a topological decomposition of X(Fg, SL2(ℂ)) derived from the decomposition ofX(PΓ) by its torus orbits. Finally, we show that the valuations coming from the closure of a maximal cell inO(g) all arise as divisorial valuations built from an associated projective compactification of X(Fg, SL2(ℂ)).

Hitchin pairs on reducible curves

We define semistable generalized parabolic Hitchin pairs (GPH) on a disjoint union [Formula: see text] of integral smooth curves and construct their moduli spaces. We define a Hitchin map on the moduli space of GPH and show that it is a proper map. We construct moduli spaces of semistable Hitchin pairs on a reducible projective curve [Formula: see text]. When [Formula: see text] is the normalization of [Formula: see text], we give a birational morphism [Formula: see text] from the moduli space [Formula: see text] of good GPH on [Formula: see text] to the moduli space [Formula: see text] of Hitchin pairs on [Formula: see text] and show that the Hitchin map on [Formula: see text] induces a proper Hitchin map on [Formula: see text]. We determine the fibers of the Hitchin maps. We study the relationship between representations of the (topological) fundamental group of [Formula: see text] and Higgs bundles on [Formula: see text]. We show that if all the irreducible components of [Formula: see text] are smooth, then the Hitchin map is defined on the entire moduli space [Formula: see text].

Framed symplectic sheaves on surfaces

A framed symplectic sheaf on a smooth projective surface [Formula: see text] is a torsion-free sheaf [Formula: see text] together with a trivialization on a divisor [Formula: see text] and a morphism [Formula: see text] satisfying some additional conditions. We construct a moduli space for framed symplectic sheaves on a surface, and present a detailed study for [Formula: see text]. In this case, the moduli space is irreducible and admits an ADHM-type description and a birational proper map onto the space of framed symplectic ideal instantons.

Nonadditive Topological Pressure of Proper Systems

We introduce a natural extension of nonadditive topological pressure for a proper map of locally compact metric spaces and properties of this new quantity are deeply and elaborately explored. In particular, a corresponding variational principle is presented.

COMPACTIFICATION OF THE PRYM MAP FOR NON-CYCLIC TRIPLE COVERINGS

According to [H. Lange and A. Ortega, Prym varieties of triple coverings, Int. Math. Res. Notices2011(22) (2011) 5045–5075], the Prym variety of any non-cyclic étale triple cover f : Y → X of a smooth curve X of genus 2 is a Jacobian variety of dimension 2. This gives a map from the moduli space of such covers to the moduli space of Jacobian varieties of dimension 2. We extend this map to a proper map Pr of a moduli space [Formula: see text] of admissible S3-covers of genus 7 to the moduli space [Formula: see text] of principally polarized abelian surfaces. The main result is that [Formula: see text] is finite surjective of degree 10.