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

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 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.

scholarly journals Finite group actions on 3-manifolds and cyclic branched covers of knots

2018 ◽  
Vol 11 (2) ◽  
pp. 283-308 ◽  
Author(s):  
Michel Boileau ◽  
Clara Franchi ◽  
Mattia Mecchia ◽  
Luisa Paoluzzi ◽  
Bruno Zimmermann
Keyword(s):  
Finite Group ◽  
Group Actions ◽  
Branched Covers ◽  
Finite Group Actions

Homology of Branched Coverings of 3-Manifolds

1992 ◽  
Vol 44 (1) ◽  
pp. 119-134
Author(s):  
John Hempel
Keyword(s):  
Classical Result ◽  
Quantitative Information ◽  
Cyclic Cover ◽  
Branched Covers ◽  
Branched Coverings ◽  
Homology Groups

AbstractWe give a relation between the homology groups H1() and H1 (M) for a branched cyclic cover → M of arbitrary closed, oriented 3-manifolds which generalizes a classical result of Plans on covers of S3 branched over a knot and provides other quantitative information as well. We include a general "free calculus" procedure for computing homology groups of branched covers and reinterpret the results in this computational setting.

Signatures of singular branched covers

1993 ◽  
Vol 295 (1) ◽  
pp. 643-659 ◽  
Author(s):  
Patrick Gilmer
Keyword(s):  
Branched Covers
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