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Softcover ISBN:  9781470436148 
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Softcover ISBN:  9781470436148 
Product Code:  MEMO/259/1249 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
eBook ISBN:  9781470452537 
Product Code:  MEMO/259/1249.E 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
Softcover ISBN:  9781470436148 
eBook ISBN:  9781470452537 
Product Code:  MEMO/259/1249.B 
List Price:  $162.00 $121.50 
MAA Member Price:  $145.80 $109.35 
AMS Member Price:  $97.20 $72.90 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 259; 2019; 78 ppMSC: Primary 57; 22
The automorphisms of a twogenerator free group \(\mathsf F_2\) acting on the space of orientationpreserving isometric actions of \(\mathsf F_2\) on hyperbolic 3space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on that plane is an invariant subsystem, which reduces to an action of a group \(\Gamma \) on \(\mathbb R ^3\) by polynomial automorphisms preserving the cubic polynomial \[ \kappa _\Phi (x,y,z) := x^{2} y^{2} + z^{2} + x y z 2 \] and an area form on the level surfaces \(\kappa _{\Phi}^{1}(k)\).

Table of Contents

Chapters

1. Introduction

2. The rank two free group and its automorphisms

3. Character varieties and their automorphisms

4. Topology of the imaginary commutator trace

5. Generalized Fricke spaces

6. Bowditch theory

7. Imaginary trace labelings

8. Imaginary characters with $k>2$

9. Imaginary characters with $k<2$.

10. Imaginary characters with $k=2$.


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The automorphisms of a twogenerator free group \(\mathsf F_2\) acting on the space of orientationpreserving isometric actions of \(\mathsf F_2\) on hyperbolic 3space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on that plane is an invariant subsystem, which reduces to an action of a group \(\Gamma \) on \(\mathbb R ^3\) by polynomial automorphisms preserving the cubic polynomial \[ \kappa _\Phi (x,y,z) := x^{2} y^{2} + z^{2} + x y z 2 \] and an area form on the level surfaces \(\kappa _{\Phi}^{1}(k)\).

Chapters

1. Introduction

2. The rank two free group and its automorphisms

3. Character varieties and their automorphisms

4. Topology of the imaginary commutator trace

5. Generalized Fricke spaces

6. Bowditch theory

7. Imaginary trace labelings

8. Imaginary characters with $k>2$

9. Imaginary characters with $k<2$.

10. Imaginary characters with $k=2$.