scholarly journals Local monodromy of branched covers and dimension of the branch set

2017 ◽  
Vol 42 ◽  
pp. 487-496 ◽  
Author(s):  
Martina Aaltonen ◽  
Pekka Pankka
Keyword(s):  
Branched Covers ◽  
Local Monodromy

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 Combinatorics of Loop Equations for Branched Covers of Sphere

2017 ◽  
Vol 2018 (18) ◽  
pp. 5638-5662 ◽  
Author(s):  
Petr Dunin-Barkowski ◽  
Nicolas Orantin ◽  
Aleksandr Popolitov ◽  
Sergey Shadrin
Keyword(s):  
Branched Covers

scholarly journals LOCAL MONODROMY OF p-ADIC DIFFERENTIAL EQUATIONS: AN OVERVIEW

2005 ◽  
Vol 01 (01) ◽  
pp. 109-154 ◽  
Author(s):  
KIRAN S. KEDLAYA
Keyword(s):  
Differential Equations ◽  
Local Monodromy ◽  
Expository Article

This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a p-adic (rigid analytic) annulus, though often with simpler proofs. These include Matsuda's classification of quasi-unipotent ∇-modules, the Christol–Mebkhout construction of the ramification filtration, and the Christol–Dwork Frobenius antecedent theorem. We also briefly discuss the p-adic local monodromy theorem without proof.

The homology of irregular dihedral branched covers ofS 3

1995 ◽  
Vol 301 (1) ◽  
pp. 519-528 ◽  
Author(s):  
James F. Davis
Keyword(s):  
Branched Covers

scholarly journals COMBINATORIAL KNOT FLOER HOMOLOGY AND DOUBLE BRANCHED COVERS

2013 ◽  
Vol 22 (06) ◽  
pp. 1350014
Author(s):  
FATEMEH DOUROUDIAN
Keyword(s):  
Floer Homology ◽  
Combinatorial Proof ◽  
Branched Covers ◽  
Knot Floer Homology ◽  
Branched Cover ◽  
Heegaard Diagram

Using a Heegaard diagram for the pullback of a knot K ⊂ S3 in its double branched cover Σ2(K), we give a combinatorial proof for the invariance of the associated knot Floer homology over ℤ.

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