Diagram Groups
Seiten
1998
American Mathematical Society (Verlag)
978-0-8218-0639-5 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-0639-5 (ISBN)
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Diagram groups are groups consisting of spherical diagrams (pictures) over monoid presentations. This work shows that the class of diagram groups contains some well-known groups, such as the R. Thompson group $F$. It develops combinatorics on diagrams similar to the combinatorics on words.
Diagram groups are groups consisting of spherical diagrams (pictures) over monoid presentations. They can be also defined as fundamental groups of the Squier complexes associated with monoid presentations. The authors show that the class of diagram groups contains some well-known groups, such as the R. Thompson group $F$. This class is closed under free products, finite direct products, and some other group-theoretical operations. The authors develop combinatorics on diagrams similar to the combinatorics on words. This helps in finding some structure and algorithmic properties of diagram groups. Some of these properties are new even for R. Thompson's group $F$. In particular, the authors describe the centralizers of elements in $F$, prove that it has solvable conjugacy problem, and more.
Diagram groups are groups consisting of spherical diagrams (pictures) over monoid presentations. They can be also defined as fundamental groups of the Squier complexes associated with monoid presentations. The authors show that the class of diagram groups contains some well-known groups, such as the R. Thompson group $F$. This class is closed under free products, finite direct products, and some other group-theoretical operations. The authors develop combinatorics on diagrams similar to the combinatorics on words. This helps in finding some structure and algorithmic properties of diagram groups. Some of these properties are new even for R. Thompson's group $F$. In particular, the authors describe the centralizers of elements in $F$, prove that it has solvable conjugacy problem, and more.
Introduction Rewrite systems Semigroup diagrams Monoid pictures Diagram groups Squier's complexes Monoid presentations and the diagram groups Diagram groups and group theoretic constructions Diagram groups over complete presentations Finitely presented diagram groups Commutator subgroups of diagram groups Asphericity Recursive presentations of diagram groups Computational complexity of the word problem in diagram groups Combinatorics on diagrams Different types of diagrams and finitely presented simple groups Open problems.
| Erscheint lt. Verlag | 30.1.1998 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Zusatzinfo | Illustrations |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 243 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-8218-0639-4 / 0821806394 |
| ISBN-13 | 978-0-8218-0639-5 / 9780821806395 |
| Zustand | Neuware |
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