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|As an application of the previous theorem we shall prove that a rectangle can be |
decomposed into finitely many nonoverlapping ... Therefore, by our previous
theorem, b/a is rational. ... The basic idea of the proof of Dehn's theorem is
|We will call this more general result the Dehn-Thurston Theorem and will derive |
the analogue of this theorem in the setting of train tracks in Theorem 3.1.1. The
remainder of this section is devoted to a discussion of Dehn's Theorem itself; ...
|So in the proofs of both the loop theorem and Dehn's lemma, covering spaces |
are used to select the switches that are to be performed, on C and D0,
respectively. As Papakyriakopoulos says of the proof of Dehn's lemma: Actually,
|There is a similar but simpler rational independence theorem for the tensor |
product R®(R discussed in the previous set of ... Dehn's theorem The regular
tetrahedron is not equidecomposable irith the cube Proof If a is a rational multiple
of n ...
|Thus, Dehn's theorem reduces the trivial link recognition problem to the free |
group recognition problem (for some class of groups). In the general case, the
free group recognition problem is undecidable. For more details see [Bir] and [BZ]
|By this exercise and the existence and the uniqueness theorems for connected |
sum decompositions, we can say that irreducible 3-manifolds are fundamental
objects in the study of 3-manifold topology. C.2 Dehn's lemma and the loop and ...
|CHAPTER 4 THE LOOP AND SPHERE THEOREMS In 1910, M. Dehn gave a "|
proof"  of a theorem which has become known as 4.1. DEHN'S LEMMA.
Suppose M is a 3-manifold and f : B2 -. M is a map such that for some
neighborhood A ...
|SCISSORS-CONGRUENCE OF POLYHEDRA AND DEHN'S THEOREM 111 The |
problem we are discussing here is called Hilbert's Third Problem. In the same
year (1900), soon after Hilbert presented the problem, his student Max Dehn ...
|The curves viewed in their entirety form a grid like graph paper which gives |
global integral coordinates. 0 Theorem 1.4.1 0 1.5. Max Dehn's contribution.
Theorem 1.5.1 (Dehn). Let R denote a rectangle that can be tiled by squares.
Then, if H is ...