Mirzakhani’s volume recursion and approach for the Witten-Kontsevich theorem on moduli tautological intersection numbers

2013 ◽  
pp. 221-266
Author(s):  
Scott Wolpert
Keyword(s):  
Intersection Numbers

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.

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

On designs with intersection numbers 0 and 2

1989 ◽  
Vol 52 (4) ◽  
pp. 407-412 ◽  
Author(s):  
V. C. Mavron ◽  
M. S. Shrikhande
Keyword(s):  
Intersection Numbers
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