## 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
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Abstract:
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.

Mathematics Subject Classification (2010): 32Q30 (primary), 14D05 (secondary)
Mathematical Reviews Number: MR3790876