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| Softcover ISBN: | 978-0-8218-0416-2 |
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| Softcover ISBN: | 978-0-8218-0416-2 |
| Product Code: | CONM/187 |
| List Price: | $130.00 |
| MAA Member Price: | $117.00 |
| AMS Member Price: | $104.00 |
| eBook ISBN: | 978-0-8218-7778-4 |
| Product Code: | CONM/187.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| Softcover ISBN: | 978-0-8218-0416-2 |
| eBook ISBN: | 978-0-8218-7778-4 |
| Product Code: | CONM/187.B |
| List Price: | $255.00 $192.50 |
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Book DetailsContemporary MathematicsVolume: 187; 1995; 196 ppMSC: Primary 20; 16
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 \(SL(2)\)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.
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Table of Contents
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Chapters
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Introduction
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Chapter 1. The Definition and Some Basic Properties of the Algebra $H[\pi ]$
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Chapter 2. ADecomposition of the Algebra $H[\pi ]$ when $\frac {1}{2}\in k$
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Chapter 3. Structure of the Algebra $H[\pi ]$ for Two-Generator Groups
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Chapter 4. Absolutely Irreducible $SL(2)$ Representations of Two-Generator Groups
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Chapter 5. Further Identities in the Algebra $H[\pi ]$ when $\frac {1}{2}\in k$
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Chapter 6. Structure of $H^{+}[\pi _{n}]$ for Free Groups $\pi _{n}$
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Chapter 7. Quaternion Algebra Localizations of $H[\pi ]$ and Absolutely Irreducible $SL(2)$ Representations
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Chapter 8. Algebro-Geometric Interpretation of SL(2) Representations of Groups
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Chapter 9. The Universal Matrix Representation of the Algebra $H[\pi ]$
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Chapter 10. Some Knot Invariants Derived from the Algebra $H[\pi ]$
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Appendix A. Addenda
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Appendix B. Afterword
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Bibliography
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Reviews
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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
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Reviews
- Requests
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 \(SL(2)\)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 Two-Generator Groups
-
Chapter 4. Absolutely Irreducible $SL(2)$ Representations of Two-Generator 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. Algebro-Geometric 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 3-manifolds from the Culler-Shalen perspective ... the monographis of considerable merit.
Zentralblatt MATH
