New PDF release: A January invitation to random groups

New PDF release: A January invitation to random groups

By Ollivier Y.

Show description

Read or Download A January invitation to random groups PDF

Similar symmetry and group books

Symmetry and heterogeneity in high temperature by Antonio Bianconi PDF

The thing of this e-book is the quantum mechanism that permits the macroscopic quantum coherence of a superconducting condensate to withstand to the assaults of hot temperature. method to this primary challenge of contemporary physics is required for the layout of room temperature superconductors, for controlling the decoherence results within the quantum desktops and for the certainty of a potential position of quantum coherence in residing subject that's debated this day in quantum biophysics.

Additional resources for A January invitation to random groups

Example text

But, just as usual small cancellation stops at density 1/12 for random groups, relative small cancellation is too restrictive and does not make it up to the maximal number of elements one can kill, hence the interest of the random point of view. b. Growth of random quotients. e. for the definition 50 A January 2005 invitation to random groups of the growth exponent). Note that by the results in [AL02], this exponent cannot stay unchanged. Theorem 39 – Let G0 be a non-elementary, torsion-free hyperbolic group generated by the finite set S.

It is possible to prove [Zuk03] quite the same hyperbolicity theorem as for the density model: Theorem 29 – If d < 1/2, then with overwhelming probability a random group in the triangular model, at density d, is non-elementary hyperbolic. If d > 1/2, it is trivial with overwhelming probability. 42 A January 2005 invitation to random groups But the fact that groups in the triangular model are “larger”than those in the density model is especially clear when considering the following proposition.

Reusing the methods of Arzhantseva and Ol’shanski˘ı, Kapovich and Schupp prove that there is “only one” m-tuple generating the group. Recall [LS77] that for a m-tuple of elements (g1 , . . , gm ) in a group, a Nielsen move consists in replacing some gi with its inverse, or interchanging two gi ’s, or replacing some gi with gi gj for some i = j. Obviously these moves do not change the subgroup generated by the m-tuple. t. which the random presentation was taken. In particular, any automorphism of G lifts to an automorphism of Fm .

Download PDF sample

Rated 4.19 of 5 – based on 37 votes
Comments are closed.