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| Operations on 3-Dimensional Small Covers |
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Citation： |
Shintarˆo KUROKI.Operations on 3-Dimensional Small Covers[J].Chinese Annals of Mathematics B,2010,31(3):393~410 |
| Page view： 1822
Net amount： 1372 |
Authors： |
Shintar?o KUROKI; |
Foundation： |
Fudan University, the Fujyukai Foundation and Basic Science Research Program
through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science
and Technology (No. 2009-0063179). |
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| Abstract： |
The purpose of this paper is to study relations among equivariant operations
on 3-dimensional small covers. The author gets three formulas for these operations. As an
application, the Nishimura’s theorem on the construction of oriented 3-dimensional small
covers and the L¨u-Yu’s theorem on the construction of all 3-dimensional small covers are
improved. Moreover, for a construction of 3-dimensional 2-torus manifolds, it is shown
that all operations can be obtained by using the equivariant surgeries. |
Keywords： |
Equivariant surgery, Finite group action, Small cover, 3-dimensional
manifold, 3-dimensional simple polytope |
Classification： |
57M50, 57M60, 57S17, 52B10 |
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