Geometric topology | Geometric group theory | Combinatorics on words

Dehn function

In the mathematical subject of geometric group theory, a Dehn function, named after Max Dehn, is an optimal function associated to a finite group presentation which bounds the area of a relation in that group (that is a freely reduced word in the generators representing the identity element of the group) in terms of the length of that relation (see pp. 79–80 in ). The growth type of the Dehn function is a quasi-isometry invariant of a finitely presented group. The Dehn function of a finitely presented group is also closely connected with non-deterministic algorithmic complexity of the word problem in groups. In particular, a finitely presented group has solvable word problem if and only if the Dehn function for a finite presentation of this group is recursive (see Theorem 2.1 in ). The notion of a Dehn function is motivated by isoperimetric problems in geometry, such as the classic isoperimetric inequality for the Euclidean plane and, more generally, the notion of a filling area function that estimates the area of a minimal surface in a Riemannian manifold in terms of the length of the boundary curve of that surface. (Wikipedia).

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What are the Inverse Trigonometric functions and what do they mean?

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From playlist Evaluate Inverse Trigonometric Functions

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Definition of a Surjective Function and a Function that is NOT Surjective

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From playlist Injective, Surjective, and Bijective Functions

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Ignat Soroko - Groups of type FP: their quasi-isometry classes and homological Dehn functions

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From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021

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From playlist 3D printing

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(New Version Available) Inverse Functions

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From playlist Exponential and Logarithmic Expressions and Equations

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From playlist Rational Functions - Understanding

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From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012

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From playlist Precalculus

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From playlist Mathematics

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From playlist Trigonometry

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From playlist Mathematics

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From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"

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From playlist How Things Work

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From playlist Trigonometry

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From playlist GED Prep Videos

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From playlist Differential Geometry

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From playlist Mathematics

Related pages

Heisenberg group | Word problem for groups | Quasi-isometry | Sectional curvature | Deterministic algorithm | Free group | Identity element | Isoperimetric inequality | Automatic group | Relatively hyperbolic group | Finitely presented group | Minimal surface | Small cancellation theory | Free abelian group | Presentation complex | Ultralimit | Nilpotent group | Riemannian manifold | Turing machine | Space complexity | Thompson groups | Van Kampen diagram | Geometric group theory | Normal closure (group theory) | Fundamental group | Equivalence relation | Higman's embedding theorem | Mapping class group | Recursion | Simply connected space