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Product Code:  CONM/187 
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Product Code:  CONM/187.E 
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Softcover ISBN:  9780821804162 
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Product Code:  CONM/187.B 
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Softcover ISBN:  9780821804162 
Product Code:  CONM/187 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9780821877784 
Product Code:  CONM/187.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821804162 
eBook ISBN:  9780821877784 
Product Code:  CONM/187.B 
List Price:  $255.00 $192.50 
MAA Member Price:  $229.50 $173.25 
AMS Member Price:  $204.00 $154.00 

Book DetailsContemporary MathematicsVolume: 187; 1995; 196 ppMSC: Primary 20; 16
This book is essentially selfcontained and requires only a basic abstract algebra course as background. The book includes and extends much of the classical theory of \(SL(2)\) representations of groups.
Readers will find \(SL(2)\)Representations of Finitely Presented Groups relevant to geometric theory of three dimensional manifolds, representations of infinite groups, and invariant theory.
Features ...
 A new finitely computable invariant \(H[\pi ]\) associated to groups and used to study the \(SL(2)\) representations of \(\pi\).
 Invariant theory and knot theory related through \(SL(2)\) representations of knot groups.
ReadershipResearchers in invariant theory, representation theory of infinite groups, and applications of group representation theory to low dimensional topology.

Table of Contents

Chapters

Introduction

Chapter 1. The Definition and Some Basic Properties of the Algebra $H[\pi ]$

Chapter 2. ADecomposition of the Algebra $H[\pi ]$ when $\frac {1}{2}\in k$

Chapter 3. Structure of the Algebra $H[\pi ]$ for TwoGenerator Groups

Chapter 4. Absolutely Irreducible $SL(2)$ Representations of TwoGenerator Groups

Chapter 5. Further Identities in the Algebra $H[\pi ]$ when $\frac {1}{2}\in k$

Chapter 6. Structure of $H^{+}[\pi _{n}]$ for Free Groups $\pi _{n}$

Chapter 7. Quaternion Algebra Localizations of $H[\pi ]$ and Absolutely Irreducible $SL(2)$ Representations

Chapter 8. AlgebroGeometric Interpretation of SL(2) Representations of Groups

Chapter 9. The Universal Matrix Representation of the Algebra $H[\pi ]$

Chapter 10. Some Knot Invariants Derived from the Algebra $H[\pi ]$

Appendix A. Addenda

Appendix B. Afterword

Bibliography


Reviews

A useful algebraic framework for students and researchers concerned with representation spaces. Apart from the contribution it offers to the algebraic insight in the topic it should be helpful especially for topologists who look at knots or 3manifolds from the CullerShalen perspective ... the monographis of considerable merit.
Zentralblatt MATH


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This book is essentially selfcontained and requires only a basic abstract algebra course as background. The book includes and extends much of the classical theory of \(SL(2)\) representations of groups.
Readers will find \(SL(2)\)Representations of Finitely Presented Groups relevant to geometric theory of three dimensional manifolds, representations of infinite groups, and invariant theory.
Features ...
 A new finitely computable invariant \(H[\pi ]\) associated to groups and used to study the \(SL(2)\) representations of \(\pi\).
 Invariant theory and knot theory related through \(SL(2)\) representations of knot groups.
Researchers in invariant theory, representation theory of infinite groups, and applications of group representation theory to low dimensional topology.

Chapters

Introduction

Chapter 1. The Definition and Some Basic Properties of the Algebra $H[\pi ]$

Chapter 2. ADecomposition of the Algebra $H[\pi ]$ when $\frac {1}{2}\in k$

Chapter 3. Structure of the Algebra $H[\pi ]$ for TwoGenerator Groups

Chapter 4. Absolutely Irreducible $SL(2)$ Representations of TwoGenerator Groups

Chapter 5. Further Identities in the Algebra $H[\pi ]$ when $\frac {1}{2}\in k$

Chapter 6. Structure of $H^{+}[\pi _{n}]$ for Free Groups $\pi _{n}$

Chapter 7. Quaternion Algebra Localizations of $H[\pi ]$ and Absolutely Irreducible $SL(2)$ Representations

Chapter 8. AlgebroGeometric Interpretation of SL(2) Representations of Groups

Chapter 9. The Universal Matrix Representation of the Algebra $H[\pi ]$

Chapter 10. Some Knot Invariants Derived from the Algebra $H[\pi ]$

Appendix A. Addenda

Appendix B. Afterword

Bibliography

A useful algebraic framework for students and researchers concerned with representation spaces. Apart from the contribution it offers to the algebraic insight in the topic it should be helpful especially for topologists who look at knots or 3manifolds from the CullerShalen perspective ... the monographis of considerable merit.
Zentralblatt MATH