Diagram groups / Victor Guba, Mark Sapir.

Format:

Book

Author/Creator:

Guba, Victor, 1962- author.

Sapir, Mark, 1957- author.

Series:

Memoirs of the American Mathematical Society ; no. 620.

Memoirs of the American Mathematical Society, 0065-9266 ; number 620

Language:

English

Subjects (All):

Geometric group theory.

Homology theory.

Physical Description:

1 online resource (130 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1997]

Language Note:

English

Summary:

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 problems, etc.

Contents:

""Contents""; ""1 Introduction""; ""2 Rewrite Systems""; ""3 Semigroup Diagrams""; ""4 Monoid Pictures""; ""5 Diagram Groups""; ""6 Squier's Complexes""; ""7 Monoid Presentations and The Diagram Groups""; ""8 Diagram Groups and Group Theoretic Constructions""; ""9 Diagram Groups over Complete Presentations""; ""10 Finitely Presented Diagram Groups""; ""11 Commutator Subgroups of Diagram Groups""; ""12 Asphericity""; ""13 Recursive Presentations of Diagram Groups""; ""14 Computational Complexity of the Word Problem in Diagram Groups""; ""15 Combinatorics on Diagrams""

""16 Different Types of Diagrams and Finitely Presented Simple Groups""""17 Open Problems""

Notes:

"November 1997, volume 130, number 620 (end of volume)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0209-2