Transformation groups of strong characteristic 0

Strong distortion in transformation groups

We discuss boundedness and distortion in transformation groups. We show that the groups Diff0(R) and Diff (Rn) have the strong distortion property, whenever 0 ≤ r ≤ ∞, r 6= n+ 1. This implies in particular that every abstract length function on these groups is bounded. With related techniques we show that, for M a closed manifold or homeomorphic to the interior of a compact manifold with bounda...

0 CHAPTER 1 Transformation Groups

ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS

In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...

Strong convergence of modified noor iteration in CAT(0) spaces

We prove a strong convergence theorem for the modified Noor iterations‎ ‎in the framework of CAT(0) spaces‎. ‎Our results extend and improve the corresponding results of‎ ‎X‎. ‎Qin‎, ‎Y‎. ‎Su and M‎. ‎Shang‎, ‎T‎. ‎H‎. ‎Kim and H‎. ‎K‎. ‎Xu and S‎. ‎Saejung‎ ‎and some others‎.

Singularities in characteristic 0 and characteristic p

1 Characteristic 0 We start with a basic question: given a polynomial f ∈ C[z1, · · · , zn] with a singularity at 0, how can we measure the “singularness” of this polynomial in a precise way? In other words: we can look at various singularities and see intuitively that some singularities are worse than others. For instance, it feels like a transverse self-intersection is probably not as bad as ...