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Combinatorial group theory and applications to geometry

Combinatorial group theory and applications to geometry

Material type
단행본
Personal Author
Collins, D. J.
Title Statement
Combinatorial group theory and applications to geometry / D.J. Collins ... [et al.].
Publication, Distribution, etc
Berlin ;   New York :   Springer ,   c1998.  
Physical Medium
240 p. : ill. ; 24 cm.
ISBN
3540637044 (acid-free paper)
General Note
"Second printing 1998 of the first edition 1993, which was originally published as Algebra VII, volume 58 of the Encyclopaedia of mathematical sciences"--T.p. verso.  
Bibliography, Etc. Note
Includes bibliographical references (p. 226-231) and indexes.
Subject Added Entry-Topical Term
Combinatorial group theory. Geometry.
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001 000045307874
005 20061122133743
008 980514s1998 gw a b 001 0 eng
010 ▼a 98150706
020 ▼a 3540637044 (acid-free paper)
035 ▼a (KERIS)REF000004717175
040 ▼a DLC ▼c DLC ▼d DLC ▼d 211009
041 1 ▼a eng ▼h rus
050 0 0 ▼a QA182.5 ▼b .C66 1998
082 0 0 ▼a 512/.2 ▼2 21
090 ▼a 512.2 ▼b C7313
245 0 0 ▼a Combinatorial group theory and applications to geometry / ▼c D.J. Collins ... [et al.].
260 ▼a Berlin ; ▼a New York : ▼b Springer , ▼c c1998.
300 ▼a 240 p. : ▼b ill. ; ▼c 24 cm.
500 ▼a "Second printing 1998 of the first edition 1993, which was originally published as Algebra VII, volume 58 of the Encyclopaedia of mathematical sciences"--T.p. verso.
504 ▼a Includes bibliographical references (p. 226-231) and indexes.
650 0 ▼a Combinatorial group theory.
650 0 ▼a Geometry.
700 1 ▼a Collins, D. J.
730 0 ▼a Algebra.
945 ▼a KINS

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Science & Engineering Library/Sci-Info(Stacks2)/ Call Number 512.2 C7313 Accession No. 121134450 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents

I. Combinatorial Group Theory and Fundamental Groups.- 1. Group Presentations and 2-Complexes.- 1.1. Presentations of Groups.- 1.2. Complexes and Fundamental Groups.- 1.3. Subgroups and Coverings.- 2. Free Groups and Free Products.- 2.1. Free Groups.- 2.2. Amalgamated Free Products and Graphs of Groups.- 2.3. Automorphisms of Free Groups.- 2.4. One-Relator Groups.- 3. Surfaces and Planar Discontinuous Groups.- 3.1. Surfaces.- 3.2. Planar Discontinuous Groups.- 3.3. Subgroups of Planar Groups.- 3.4. Automorphisms of Fuchsian Groups.- 3.5. Relations to Other Theories of Surfaces.- 4. Cancellation Diagrams and Equations Over Groups.- 4.1. Cancellation Diagrams.- 4.2. Locally Indicable Groups and Equations Over Groups.- 5. 3-Manifolds and Knots.- 5.1. Fundamental Groups of 3-Manifolds.- 5.2. Haken Manifolds.- 5.3. On Knots and Their Groups.- 6. Cohomological Methods and Ends.- 6.1. Group Extensions and Cohomology.- 6.2. Ends of Groups.- 7. Decision Problems.- 7.1. Decision Problems and Algorithms.- 7.2. Unsolvable Decision Problems.- 7.3. Automata and Groups.- Index of Notation.- II. Some Questions of Group Theory Related to Geometry.- 1. Equations in Groups and Some Related Questions.- 1. Basic Concepts and the Theorem of Makanin.- 2. Solutions of Systems and Homomorphisms.- 3. Fundamental Sequences and Razborov's Theorem.- 4. On the Structure of the Set of Solutions of Quadratic Equations in Free Groups.- 5. Coefficient-Free Quadratic Equations.- 6. The Classification of Epimorphisms from Surface Groups to Free Groups.- 7. On the Minimal Number of Fixed Points in the Homotopy Class of Mappings and the Width of Elements in Free Groups.- 8. On Quadratic Equations in Hyperbolic Groups.- 2. Splitting Homomorphisms and Some Problems in Topology.- 1. Heegaard Decompositions of 3-Manifolds and their Equivalence.- 2. The Poincare Conjecture and Three Algorithmic Problems Connected with 3-Manifolds.- 3. Information on Aut ?1(T) and Some of its Subgroups and Factor Groups.- 4. On the Problem of the Equivalence of Splitting Homomorphisms.- 5. On an Algebraic Reduction of the Poincare Conjecture and the Algorithmic Poincare Problem.- 6. Some Analogues with the Group of Symplectic Matrices and the Torelli Group.- 7. Algebraic Reduction of the Problem of the Equivalence of Links.- 8. On the Andrews-Curtis Conjecture.- 3. On the Rate of Growth of Groups and Amenable Groups.- 1. On the Growth of Graphs and of Riemannian Manifolds.- 2. On the Notion of Growth of a Finitely Generated Group.- 3. On the Proof of Gromov's Theorem and Some Related Results.- 4. Example of a Group of Intermediate Growth and the Construction Scheme of such a Group.- 5. On the Structure of the Set of Growth Degrees of Groups that are Residually-p Groups.- 6. On an Application of the Theory of Groups of Polynomial Growth to Geometry.- 7. Regularly Filtered Surfaces and Amenable Groups.- Index of Notation.- Author Index.


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