Euclidean Symmetry of Closed Surfaces Immersed in 3-Space, Part II

Thomas Tucker
Colgate University

Undine Leopold
Technische Univerit\" at of Chemnitz



Content: Given a finite group $G$ of orientation-preserving isometries of euclidean 3-space $E^3$ and a closed surface $S$, an immersion $f: S\rightarrow E^3$ is in $G$-general position if $f(S)$ is invariant under $G$, points of $S$ have disk neighborhoods whose images are in general position, and no singular points of $f(S)$ lie on an axis of rotation of $G$. For such an immersion, there is an induced action of $G$ on $S$ whose Riemann-Hurwitz equation satisfies certain natural restrictions. We classify which restricted Riemann-Hurwitz equations are realized by a $G$-general position immersion of $S$. In this part of the talk, we focus on the low-dimensional topology of immersions of the quotient surface $S/G$ in the orbifold $E^3/G$

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