Geometric group theory

Geometric group theory and combinatorial group theory are two closely related branches of mathematics, which study infinite discrete groups.

Related Topics:
Mathematics - Discrete group

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Geometric group theory uses topological and geometric methods to study groups; the main philosophy is to deduce information about a group by analyzing how it acts on topological spaces. Combinatorial group theory studies discrete groups as quotients of free groups, typically described using presentations.

Related Topics:
Topological - Geometric - Acts - Topological space - Quotients - Free group - Presentations

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In the early 20th century, pioneering work of Dehn,

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Nielsen, Reidemeister and

Related Topics:
Nielsen - Reidemeister

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Schreier amongst others established a close correspondence between the two subjects. While

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some problems and methods are still discernably "more geometric" or "more combinatorial" than others, the fields are inextricably intertwined; they are now generally considered the same area of mathematics. Other closely related fields include algebraic topology, geometric topology and computational group theory.

Related Topics:
Algebraic topology - Geometric topology - Computational group theory

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