scholarly journals Volumes of 3-ball quotients as intersection numbers

2019 ◽  
Vol 373 (1) ◽  
pp. 343-383 ◽  
Author(s):  
Martin Deraux
Keyword(s):  
Intersection Numbers ◽  
Ball Quotients

Pseudo-Anosov Theory

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Braid Groups ◽  
Intersection Numbers ◽  
Branched Covers ◽  
Algebraic Integers ◽  
Dehn Twists ◽  
Mapping Classes ◽  
Dynamical Properties

This chapter focuses on the construction as well as the algebraic and dynamical properties of pseudo-Anosov homeomorphisms. It first presents five different constructions of pseudo-Anosov mapping classes: branched covers, constructions via Dehn twists, homological criterion, Kra's construction, and a construction for braid groups. It then proves a few fundamental facts concerning stretch factors of pseudo-Anosov homeomorphisms, focusing on the theorem that pseudo-Anosov stretch factors are algebraic integers. It also considers the spectrum of pseudo-Anosov stretch factors, along with the special properties of those measured foliations that are the stable (or unstable) foliations of some pseudo-Anosov homeomorphism. Finally, it describes the orbits of a pseudo-Anosov homeomorphism as well as lengths of curves and intersection numbers under iteration.

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

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yongqiang Liu ◽  
Laurenţiu Maxim ◽  
Botong Wang
Keyword(s):  
Integral Homology ◽  
Algebraic Varieties ◽  
Finiteness Property ◽  
Rational Homology ◽  
Mellin Transformation ◽  
Hopf Conjecture ◽  
Ball Quotients ◽  
Proper Map ◽  
Complex Projective ◽  
Aspherical Manifolds

Abstract 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.

scholarly journals Intersection Numbers of Heegner Divisors on Shimura Curves

2008 ◽  
Vol 4 (4) ◽  
pp. 1165-1204
Author(s):  
Kevin Keating ◽  
David P. Roberts
Keyword(s):  
Shimura Curves ◽  
Intersection Numbers

scholarly journals Intersection numbers on the relative Hilbert schemes of points on surfaces

2017 ◽  
Vol 21 (3) ◽  
pp. 531-542 ◽  
Author(s):  
Amin Gholampour ◽  
Artan Sheshmani
Keyword(s):  
Hilbert Schemes ◽  
Intersection Numbers
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