mathematical subject of geometric group theory, a Dehn function, named after Max Dehn, is an optimal function associated to a finite group presentation which...

been named for Dehn. Among them: Dehn's rigidity theorem Dehn invariant Dehn's algorithm Dehn's lemma Dehn plane Dehn surgery Dehn twist Dehn–Sommerville...

easy to see that Dehn(n) is an isoperimetric function for (†) and, moreover, if f(n) is any other isoperimetric function for (†) then Dehn(n) ≤ f(n) for...

growth rate of a finitely generated group; the isoperimetric function or Dehn function of a finitely presented group; the number of ends of a group;...

his geometries, Dehn used a non-Archimedean ordered Pythagorean field Ω(t), a Pythagorean closure of the field of rational functions R(t), consisting...

In topology, a branch of mathematics, a Dehn surgery, named after Max Dehn, is a construction used to modify 3-manifolds. The process takes as input a...

and practices. Oxford University Press. pp. 467–68. ISBN 978-0199928460. Dehn, Milton J (2011). Working memory and academic learning: Assessment and intervention...

In geometry, the Dehn invariant is a value used to determine whether one polyhedron can be cut into pieces and reassembled ("dissected") into another,...

of free groups of rank ≥ 3 {\displaystyle \geq 3} have exponential Dehn function, and hence (see below) are not CAT(0). Let G {\displaystyle G} be a...

Cayley 2-complex of a finite presentation, they are equivalent to the Dehn function of the group presentation. They are invariant under quasi-isometries...

some remarkable properties regarding its finite quotient groups, its Dehn function and the complexity of its word problem. The group is given by the presentation...

hyperbolic Dehn surgery is an operation by which one can obtain further hyperbolic 3-manifolds from a given cusped hyperbolic 3-manifold. Hyperbolic Dehn surgery...

or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are...

not always possible. This was confirmed within the year by his student Max Dehn, who proved that the answer in general is "no" by producing a counterexample...

finite index). This has many further consequences, for example: the Dehn function of a finitely generated linear group can only be either polynomial or...

curves on these surfaces. The earliest contributors were Max Dehn and Jakob Nielsen: Dehn proved finite generation of the group, and Nielsen gave a classification...

various notions of nonpositive curvature for groups (CAT(0) groups, Dehn functions, automaticity...), right angled Artin groups, and topics close to combinatorial...

American science fiction film directed by Don Taylor and written by Paul Dehn. The film is the sequel to Beneath the Planet of the Apes (1970) and the...

appears between certain Dehn twists in the mapping class group of a surface. The most general version of the relation involves seven Dehn twists. The relation...

embeds as a subgroup of a finitely presented group with polynomial Dehn function. A combined featured review of these two papers in Mathematical Reviews...

characteristic, duality, vertex figures, surface area, volume, interior lines, Dehn invariant, and symmetry. The symmetry of a polyhedron means that the polyhedron's...

algebraic combinatorics, a quasisymmetric function is any element in the ring of quasisymmetric functions which is in turn a subring of the formal power...

) {\displaystyle f(cx)\neq cf(x)} are known as Cauchy-Hamel functions and are used in Dehn-Hadwiger invariants which are used in the extension of Hilbert's...

Consequently, there are at most three Dehn fillings of M with cyclic fundamental group. Thurston's hyperbolic Dehn surgery theorem states: M ( u 1 , u 2...

powerful results and methods. For example, he was able to show that all but ten Dehn surgeries on the figure-eight knot resulted in non-Haken, non-Seifert-fibered...

155–160. doi:10.1016/1352-2310(95)00143-M. Sheridan, M.F.; Wohletz, K.H.; Dehn, J. (1987). "Discrimination of grain-size subpopulations in pyroclastic deposits"...

field, the hyperreal numbers, the surreal numbers, the Dehn field, and the field of rational functions with real coefficients (where we define f > g to mean...

group generated by Dehn twists; this has been proved by Max Dehn, W. B. R. Lickorish, and Allen Hatcher).[citation needed] Max Dehn and Jakob Nielsen showed...

Olshanskii has focused on asymptotic invariants of groups, such as Dehn functions, distortion, and relative subgroup growth. These invariants are connected...

the products of edge lengths with exterior dihedral angles, is a function of the Dehn invariant that is also known to stay constant while a polyhedron...