## Dehn Twists, Hypertwists, and Uniformization of Twined Singularities

J. Math. Sci. Univ. Tokyo
Vol. 25 (2018), No. 1, Page 35-90.

Sasaki, Kenjiro ; Takamura, Shigeru
Dehn Twists, Hypertwists, and Uniformization of Twined Singularities
There are two kinds of homeomorphisms of an annulus that appear as local monodromies of degenerations of Riemann surfaces: fractional Dehn twist and Nielsen twist. In this paper, they are “in a unified way” generalized to higher dimensions as a hypertwist, which is the monodromy of a twined singularity (a quotient of a multiplicative $A$-singularity). We moreover establish the uniformization theorem of this quotient, which generalizes the uniformization theorem in our previous paper.
Keywords: Uniformization of singularity, Cyclic quotient, Group action, Multiplicative $A$-singularity, Monodromy, Fractional Dehn twist, Small group, Lifting and descent.