 About 1,030 results  books.google.com 2.1.4 A Proof of the DehnNielsen Theorem Let us begin with the following
definition. Suppose that X and Y are 2 orbifolds and that f:X — > Y is a
continuous map between the underlying topological spaces. We say that f is an
orbifold map if ... 

 books.google.com by Fenchel and an English translation was published in Nielsen's Collected
Mathematical Papers (1986). The notes credit the theorem to Dehn and say that
Dehn's proof uses the idea from Poincaré (1904) of lifting curves to the universal
... 

 books.google.com We have the following remarkable theorem. THEOREM 8.1 (Dehn–Nielsen–Baer
) Let g ≥ 1. The homomorphism σ : Mod±(Sg) −→ Out(π1(Sg)) is an isomorphism
. As noted above, the proof of Theorem 8.1 reduces to the statement that σ is ... 

 books.google.com It is faithful, more precisely: Theorem 2.19 (Artin [7], [8]). (1) The Artin ... The first
way uses the FadellNeuwirth fiber bundle p: Mn+\ »□ M„ of Theorem 2.10. Let
Sym„ act ... In this setting, it is known as the DehnNielsenBaer theorem. Here is
a ... 

 books.google.com For closed S, the surjectivity part of these theorems is due to Dehn, who did not
publish his proof, and to Nielsen [191], who published a proof partially based on
Dehn's ideas. Another proof was suggested by Seifert [211]. The injectivity part is
... 

 books.google.com DehnNielsen Theorem. An automorphism a of the fundamental group G of a
compact surface is induced by a homeomorphism of the surface if and only if Q(si
) = wis^w^l . 1 < i fc < m. In this case (^ '",!") is a permutation and wi C G, w(u>i)ei
... 

 books.google.com Since both result from systems of cuts of the surface S and these systems are of
the same type it follows that there is a homeomorphism inducing a: 3.4.6. Dehn
Nielsen Theorem. An automorphism a of the fundamental group G of a compact ... 

 books.google.com In this case, by Theorem 1.4 (or Theorem 2.14) below, Modg,p and Mod+g,p are
not isomorphic to Out(π1(Sg,p)), and hence the exact analogue of DehnNielsen
theorem does not hold. On the other hand, a modification holds by requiring that
... 

 books.google.com is an inner automorphism of tti(M), and so [ft*] = 1. Thus, the mapping h t— > [ft*]
induces a function v : Map(M) > Out(?ri(M)). The next theorem is a basic theorem
of surface theory. Theorem 9.4.3. (The DehnNielsen Theorem) If M is a closed ... 

 books.google.com width of 70 collar theorems 94,97, 106, 112 color 298 commensurable 336
complete sequence 379 completely ... 111 cut open 15 cycle 313 defining
relation 164, 171, 179 D Dehn twist 72,425 DehnNielsen theorem 171 direct 156
Dirichlet ... 

 