**Contemporary Mathematics**

Volume: 187;
1995;
196 pp;
Softcover

MSC: Primary 20; 16;

**Print ISBN: 978-0-8218-0416-2
Product Code: CONM/187**

List Price: $67.00

AMS Member Price: $53.60

MAA Member Price: $60.30

**Electronic ISBN: 978-0-8218-7778-4
Product Code: CONM/187.E**

List Price: $63.00

AMS Member Price: $50.40

MAA Member Price: $56.70

# \(SL(2)\) Representations of Finitely Presented Groups

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*G. W. Brumfiel; H. M. Hilden*

This book is essentially self-contained 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 \(SL(2)\)

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.

#### Readership

Researchers in invariant theory, representation theory of infinite groups, and applications of group representation theory to low dimensional topology.

#### Reviews & Endorsements

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 3-manifolds from the Culler-Shalen perspective … the monographis of considerable merit.

-- Zentralblatt MATH

# Table of Contents

## $SL(2)$ Representations of Finitely Presented Groups

- Contents vii8 free
- Introduction 110 free
- Chapter 1. The Definition and Some Basic Properties of the Algebra H[π] 1524
- Chapter 2. A Decomposition of the Algebra H[π] when ½ ε k 2130
- Chapter 3. Structure of the Algebra H[π] for Two-Generator Groups 2938
- Chapter 4. Absolutely Irreducible SL(2) Representations of Two-Generator Groups 3948
- Chapter 5. Further Identities in the Algebra H[π] when ½ Є k 4756
- Chapter 6. Structure of H+[πn] for Free Groups πn 5968
- Chapter 7. Quaternion Algebra Localizations of H[π] and Absolutely Irreducible SL(2) Representations 6978
- Chapter 8. Algebro-Geometric Interpretation of SL(2) Representations of Groups 8392
- Chapter 9. The Universal Matrix Representation of the Algebra H[π] 8998
- Chapter 10. Some Knot Invariants Derived from the Algebra H[π] 101110
- Appendix A. Addenda 107116
- Appendix B. Afterword 183192
- Bibliography 195204