scholarly journals Small intersection numbers in the curve graph

2014 ◽  
Vol 46 (5) ◽  
pp. 989-1002 ◽  
Author(s):  
Tarik Aougab ◽  
Samuel J. Taylor
Keyword(s):  
Intersection Numbers ◽  
Curve Graph

scholarly journals Distances and Intersections of Curves

2018 ◽  
Vol 2020 (23) ◽  
pp. 9674-9693
Author(s):  
Yohsuke Watanabe
Keyword(s):  
Intersection Number ◽  
Intersection Numbers ◽  
Dehn Twists ◽  
Curve Graph ◽  
Mapping Classes

Abstract We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we study intersection numbers of curves contained in geodesics in the curve graph. Furthermore, we generalize a well-known result on intersection number growth of curves under iteration of Dehn twists and multitwists for all kinds of pure mapping classes.

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.

EXHAUSTION OF THE CURVE GRAPH VIA RIGID EXPANSIONS

2018 ◽  
Vol 61 (1) ◽  
pp. 195-230 ◽  
Author(s):  
JESÚS HERNÁNDEZ HERNÁNDEZ
Keyword(s):  
Topological Type ◽  
Orientable Surface ◽  
Finite Topological Type ◽  
Curve Graph ◽  
Finite Set ◽  
Rigid Set

AbstractFor an orientable surfaceSof finite topological type with genusg≥ 3, we construct a finite set of curves whose union of iterated rigid expansions is the curve graph$\mathcal{C}$(S). The set constructed, and the method of rigid expansion, are closely related to Aramayona and Leiniger's finite rigid set in Aramayona and Leininger,J. Topology Anal.5(2) (2013), 183–203 and Aramayona and Leininger,Pac. J. Math.282(2) (2016), 257–283, and in fact a consequence of our proof is that Aramayona and Leininger's set also exhausts the curve graph via rigid expansions.

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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