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Full-Text Articles in Physical Sciences and Mathematics
Finite Symmetries Of S^4, Weimin Chen Chen, Slawomir Kwasik, Reinhard Shultz
Finite Symmetries Of S^4, Weimin Chen Chen, Slawomir Kwasik, Reinhard Shultz
Weimin Chen
This paper discusses topological and locally linear actions of finite groups on S4. Local linearity of the orientation preserving actions on S4 forces the group to be a subgroup of SO(5). On the other hand, orientation reversing topological actions of “exotic” groups G (i.e. G 6⊂ O(5)) on S4 are constructed, and local linearity and stable smoothability of the actions are studied.
G-Minimality And Invariant Negative Spheres In G-Hirzenbruch Surfaces, Weimin Chen Chen
G-Minimality And Invariant Negative Spheres In G-Hirzenbruch Surfaces, Weimin Chen Chen
Weimin Chen
In this paper we initiate a study on the notion of G-minimality of four-manifolds equipped with an action of a finite group G. Our work shows that even in the case of cyclic actions on CP2#CP2, the comparison of G-minimality in the various categories (i.e., locally linear, smooth, symplectic) is already a delicate and interesting problem. In particular, we show that if a symplectic Zn-action on CP2#CP2 has an invariant locally linear topological (−1)-sphere, then it must admit an invariant symplectic (−1)-sphere, provided that n = 2 or n is odd. For the case where n > 2 and even, the …